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Calculators

Every exam formula, interactive. Enter your numbers and get the verdict — not just the number.

Cost Calculator

Total investment for any certification — exam fees, membership math and prep costs.

Open cost calculator

Composite calculators

Multi-output panels that answer a whole exam question in one pass.

EVM Suite

Enter BAC, EV, PV and AC once — get CPI, SPI, CV, SV, EAC, ETC, VAC and TCPI together.

Fill in all four values to see the full earned-value picture.

Placeholders show the worked example values — press Enter to commit a field.

Sigma Level

Convert defects, units and opportunities into DPMO, process yield and a sigma band.

Enter defects, units and opportunities per unit.

Placeholders show the worked example values — press Enter to commit a field.

PERT Estimate

Three-point beta-PERT estimate with standard deviation and a ±1σ confidence range.

Enter all three estimates.

Placeholders show the worked example values — press Enter to commit a field.

Formula calculators

46 interactive formulas grouped by field.

Business Analysis

4 formulas

Expected Monetary Value

EMV = Probability x Impact

P
Probability of the event (%)
I
Monetary impact if it occurs (USD)
  • > 0 — Net opportunity
  • = 0 — Neutral
  • < 0 — Net threat

Worked example

A vendor integration has a 30% chance of a late delivery that would cost $80,000 in rework and penalties.

EMV = 0.30 x -80,000 = -24,000

Reserve $24,000 of contingency for this single risk, or spend less than that to mitigate it.

Try: A vendor integration has a 30% chance of a late delivery that would cost $80,000 in rework and penalties.

Three-Point (Beta) Estimate for requirements effort

E = (O + 4M + P) / 6

O
Optimistic effort (hours)
M
Most likely effort (hours)
P
Pessimistic effort (hours)
  • > 0 — Weighted estimate

Worked example

Eliciting and documenting requirements for a payments module: optimistic 60 hours, most likely 90 hours, pessimistic 150 hours.

E = (60 + 4x90 + 150) / 6 = 95

Commit to 95 hours and communicate a 80-110 hour one-sigma range to the sponsor.

Try: Eliciting and documenting requirements for a payments module: optimistic 60 hours, most likely 90 hours, pessimistic 150 hours.

Cost-Benefit Ratio

BCR = Total benefits / Total costs

B
Total discounted benefits (USD)
C
Total discounted costs (USD)
  • > 1.5 — Strong business case
  • 1 - 1.5 — Marginal business case
  • < 1 — Not justified

Worked example

A self-service portal is forecast to deliver $1,800,000 of discounted benefits against $1,000,000 of discounted costs.

BCR = 1,800,000 / 1,000,000 = 1.8

Every dollar spent returns $1.80 of benefit — a strong case that survives moderate estimate error.

Try: A self-service portal is forecast to deliver $1,800,000 of discounted benefits against $1,000,000 of discounted costs.

Weighted Scoring Model (3 criteria)

Score = SUM(weight x rating) / SUM(weight)

w1..w3
Weight of each criterion (weight)
s1..s3
Rating of the option against each criterion (1-10)
  • > 7.5 — Strong fit
  • 5 - 7.5 — Acceptable fit
  • < 5 — Weak fit

Worked example

Selecting a CRM. Criteria: functional fit (weight 5, rated 8), total cost (weight 3, rated 6), integration effort (weight 2, rated 4).

Score = (5x8 + 3x6 + 2x4) / (5 + 3 + 2) = 66 / 10

An acceptable but not standout option — the low integration rating is what pulls it down.

Try: Selecting a CRM.

Project Management

12 formulas

Cost Performance Index

CPI = EV / AC

EV
Earned Value (USD)
AC
Actual Cost (USD)
  • CPI > 1.0 — Under budget
  • CPI = 1.0 — On budget
  • CPI < 1.0 — Over budget

Worked example

An office fit-out has a $400,000 budget. At the end of month 3 the team has completed 45% of the planned scope and spent $210,000.

CPI = 180,000 / 210,000 = 0.857

The project earns only 86 cents of value per dollar spent — roughly 14% cost overrun if the trend holds.

Try: An office fit-out has a $400,000 budget.

Schedule Performance Index

SPI = EV / PV

EV
Earned Value (USD)
PV
Planned Value (USD)
  • SPI > 1.0 — Ahead of schedule
  • SPI = 1.0 — On schedule
  • SPI < 1.0 — Behind schedule

Worked example

A software rollout planned $250,000 of work by week 10 but has earned $220,000 of value.

SPI = 220,000 / 250,000 = 0.88

The team is delivering at 88% of planned pace — about 1.2 weeks behind after 10 weeks.

Try: A software rollout planned $250,000 of work by week 10 but has earned $220,000 of value.

Cost Variance

CV = EV - AC

EV
Earned Value (USD)
AC
Actual Cost (USD)
  • CV > 0 — Under budget
  • CV = 0 — On budget
  • CV < 0 — Over budget

Worked example

Same office fit-out: EV $180,000 against AC $210,000.

CV = 180,000 - 210,000 = -30,000

The project is $30,000 over budget for the work completed so far.

Try: Same office fit-out: EV $180,000 against AC $210,000.

Schedule Variance

SV = EV - PV

EV
Earned Value (USD)
PV
Planned Value (USD)
  • SV > 0 — Ahead of schedule
  • SV = 0 — On schedule
  • SV < 0 — Behind schedule

Worked example

Software rollout: EV $220,000 against PV $250,000 at week 10.

SV = 220,000 - 250,000 = -30,000

$30,000 worth of planned work has not been delivered yet.

Try: Software rollout: EV $220,000 against PV $250,000 at week 10.

Estimate at Completion (CPI method)

EAC = BAC / CPI

BAC
Budget at Completion (USD)
CPI
Cost Performance Index (index)
  • EAC > BAC — Forecast overrun
  • EAC = BAC — On plan
  • EAC < BAC — Forecast underrun

Worked example

Office fit-out with BAC $400,000 running at CPI 0.86.

EAC = 400,000 / 0.857 = 466,744

Expect roughly $67,000 of overrun unless cost efficiency improves.

Try: Office fit-out with BAC $400,000 running at CPI 0.

Estimate to Complete

ETC = EAC - AC

EAC
Estimate at Completion (USD)
AC
Actual Cost to date (USD)
  • ETC > remaining budget (BAC - AC) — Additional funds needed
  • ETC <= remaining budget — Fundable from baseline

Worked example

Office fit-out: EAC $466,700 with $210,000 already spent.

ETC = 466,700 - 210,000 = 256,700

$256,700 more is needed, versus $190,000 of budget remaining — a $66,700 funding gap.

Try: Office fit-out: EAC $466,700 with $210,000 already spent.

Variance at Completion

VAC = BAC - EAC

BAC
Budget at Completion (USD)
EAC
Estimate at Completion (USD)
  • VAC > 0 — Forecast saving
  • VAC = 0 — On budget
  • VAC < 0 — Forecast overrun

Worked example

Office fit-out: BAC $400,000, EAC $466,700.

VAC = 400,000 - 466,700 = -66,700

Raise a change request for roughly $67,000 or cut scope now.

Try: Office fit-out: BAC $400,000, EAC $466,700.

To-Complete Performance Index

TCPI = (BAC - EV) / (BAC - AC)

BAC
Budget at Completion (USD)
EV
Earned Value (USD)
AC
Actual Cost (USD)
  • TCPI < 1.0 — Achievable
  • TCPI = 1.0 — Exactly on plan
  • TCPI > 1.0 — Hard to achieve

Worked example

Office fit-out: BAC $400,000, EV $180,000, AC $210,000.

TCPI = (400,000 - 180,000) / (400,000 - 210,000) = 220,000 / 190,000 = 1.158

The team must work 16% more cost-efficiently than planned for the rest of the project — unlikely at CPI 0.86.

Try: Office fit-out: BAC $400,000, EV $180,000, AC $210,000.

PERT Three-Point Estimate (Beta)

E = (O + 4M + P) / 6

O
Optimistic duration or cost (days)
M
Most likely duration or cost (days)
P
Pessimistic duration or cost (days)
  • E close to M — Balanced risk
  • E noticeably > M — Downside-heavy
  • E noticeably < M — Upside-heavy

Worked example

A data-migration task is estimated at 8 days optimistic, 12 days most likely, 26 days pessimistic.

E = (8 + 4x12 + 26) / 6 = 82 / 6 = 13.67

Plan 14 days, not 12 — the long tail adds nearly two days of expected duration.

Try: A data-migration task is estimated at 8 days optimistic, 12 days most likely, 26 days pessimistic.

PERT Standard Deviation

SD = (P - O) / 6

P
Pessimistic estimate (days)
O
Optimistic estimate (days)
  • SD small relative to E (< 10%) — Tight estimate
  • SD 10-25% of E — Moderate uncertainty
  • SD > 25% of E — High uncertainty

Worked example

Same data-migration task: O = 8 days, P = 26 days, E = 13.7 days.

SD = (26 - 8) / 6 = 3.0

There is ~95% confidence the task lands between 7.7 and 19.7 days (E ± 2 SD) — commit to 20 days externally.

Try: Same data-migration task: O = 8 days, P = 26 days, E = 13.

Communication Channels

Channels = n(n - 1) / 2

n
Number of stakeholders in the communication network (people)
  • Up to ~15 channels — Informal works
  • 15-60 channels — Needs structure
  • Over 60 channels — Communication overhead risk

Worked example

A steering group has 9 members and two new directors join.

Before: 9x8/2 = 36. After: 11x10/2 = 55.

Adding two people adds 19 communication paths — formalise the reporting structure.

Try: A steering group has 9 members and two new directors join.

Total Float (Slack)

TF = LS - ES = LF - EF

LS
Late Start (day)
ES
Early Start (day)
LF
Late Finish (day)
EF
Early Finish (day)
  • TF = 0 — Critical activity
  • TF > 0 — Has slack
  • TF < 0 — Negative float

Worked example

Activity D on a non-critical path: ES day 12, EF day 17, LS day 19, LF day 24.

TF = 19 - 12 = 7 (and 24 - 17 = 7)

Activity D can slip up to 7 days before it becomes critical — a safe place to borrow resources from.

Try: Activity D on a non-critical path: ES day 12, EF day 17, LS day 19, LF day 24.

Human Resources

6 formulas

Employee Turnover Rate

Turnover % = (Separations in period / Average headcount) x 100

S
Separations during the period (employees)
AH
Average headcount for the period (employees)
  • < 10% annual — Low
  • 10-20% annual — Typical
  • > 20% annual — High

Worked example

A company starts the year with 480 employees, ends with 520, and 78 people leave.

Average headcount = (480 + 520) / 2 = 500; Turnover = 78 / 500 x 100 = 15.6

Mid-range overall — but if 50 of the 78 came from one function, that team is the real problem.

Try: A company starts the year with 480 employees, ends with 520, and 78 people leave.

Cost per Hire

CPH = (Internal recruiting costs + External recruiting costs) / Number of hires

IC
Internal costs (recruiter salaries, referral bonuses, ATS) (USD)
EC
External costs (agencies, job boards, assessments, travel) (USD)
H
Hires in the period (hires)
  • Below industry benchmark — Efficient
  • Around benchmark — Normal
  • Well above benchmark — Expensive

Worked example

A team hires 25 people in a quarter with $60,000 of internal recruiting cost and $115,000 of agency and job-board spend.

CPH = (60,000 + 115,000) / 25 = 175,000 / 25 = 7,000

Two-thirds of the cost is external — moving 20% of hires to referrals would save roughly $23,000 a quarter.

Try: A team hires 25 people in a quarter with $60,000 of internal recruiting cost and $115,000 of agency and job-board spend.

Absenteeism Rate

Absenteeism % = (Unscheduled absence days / (Headcount x Available workdays)) x 100

A
Unscheduled absence days in the period (days)
N
Average headcount (employees)
W
Scheduled workdays per employee in the period (days)
  • < 1.5% — Low
  • 1.5-3.0% — Normal
  • > 3.0% — High

Worked example

200 employees, 21 workdays in the month, 84 unscheduled absence days recorded.

Absenteeism = 84 / (200 x 21) x 100 = 84 / 4,200 x 100 = 2.0

Within the normal band; segment by shift before launching any intervention.

Try: 200 employees, 21 workdays in the month, 84 unscheduled absence days recorded.

Revenue per Employee

RPE = Total revenue / Average headcount

R
Total revenue for the period (USD)
AH
Average headcount (employees)
  • Rising year on year — Improving productivity
  • Flat — Scaling linearly
  • Falling — Productivity dilution

Worked example

A services firm reports $84,000,000 revenue with an average headcount of 420.

RPE = 84,000,000 / 420 = 200,000

Track it quarterly next to cost per hire — hiring 40 more people needs $8M of new revenue to hold the ratio.

Try: A services firm reports $84,000,000 revenue with an average headcount of 420.

HR-to-Employee Ratio

Ratio = (HR full-time equivalents / Total employees) x 100

HRFTE
HR staff (full-time equivalents) (FTE)
E
Total employees (employees)
  • < 1.0 per 100 — Lean HR function
  • 1.0-1.5 per 100 — Typical
  • > 2.0 per 100 — HR-heavy

Worked example

An organisation of 800 employees has 9 HR FTEs.

Ratio = 9 / 800 x 100 = 1.125

Right at benchmark — further HR hiring should be justified by service levels, not headcount growth alone.

Try: An organisation of 800 employees has 9 HR FTEs.

Time to Fill (average)

Average Time to Fill = Sum of days from requisition approval to offer acceptance / Number of positions filled

Dn
Days from requisition opening to offer acceptance for each role (days)
P
Positions filled in the period (positions)
  • < 30 days — Fast
  • 30-45 days — Typical
  • > 60 days — Slow

Worked example

Five roles filled in 28, 34, 41, 52 and 60 days.

Sum = 215 days; Average = 215 / 5 = 43

The 60-day outlier is a senior role — report median alongside mean so one hard requisition does not distort the story.

Try: Five roles filled in 28, 34, 41, 52 and 60 days.

AI & Cloud

5 formulas

Accuracy

Accuracy = (TP + TN) / (TP + TN + FP + FN) x 100

TP
True positives (count)
TN
True negatives (count)
FP
False positives (count)
FN
False negatives (count)
  • > 90 — High accuracy
  • 70 - 90 — Moderate accuracy
  • < 70 — Low accuracy

Worked example

A support-ticket classifier is evaluated on 1,000 tickets: 380 true positives, 520 true negatives, 60 false positives and 40 false negatives.

Accuracy = (380 + 520) / 1,000 x 100 = 90%

Nine in ten tickets are routed correctly, but the 40 missed positives may matter more than the headline number.

Try: A support-ticket classifier is evaluated on 1,000 tickets: 380 true positives, 520 true negatives, 60 false positives and 40 false negatives.

Precision

Precision = TP / (TP + FP) x 100

TP
True positives (count)
FP
False positives (count)
  • > 90 — Very precise
  • 70 - 90 — Moderate precision
  • < 70 — Low precision

Worked example

The same classifier flagged 440 tickets as urgent; 380 truly were.

Precision = 380 / (380 + 60) x 100 = 86.36%

About one in seven urgent flags is a false alarm — acceptable for triage, too high for auto-escalation.

Try: The same classifier flagged 440 tickets as urgent; 380 truly were.

Recall (Sensitivity)

Recall = TP / (TP + FN) x 100

TP
True positives (count)
FN
False negatives (count)
  • > 90 — High recall
  • 70 - 90 — Moderate recall
  • < 70 — Low recall

Worked example

There were 420 genuinely urgent tickets; the classifier caught 380 and missed 40.

Recall = 380 / (380 + 40) x 100 = 90.48%

Nine in ten urgent tickets are caught; the 40 missed cases are the ones to investigate for a pattern.

Try: There were 420 genuinely urgent tickets; the classifier caught 380 and missed 40.

F1 Score

F1 = 2 x (Precision x Recall) / (Precision + Recall)

Precision
Precision (%)
Recall
Recall (%)
  • > 90 — Excellent balance
  • 70 - 90 — Acceptable balance
  • < 70 — Poor balance

Worked example

The ticket classifier scores 86.4% precision and 90.5% recall.

F1 = 2 x (86.36 x 90.48) / (86.36 + 90.48) = 88.37

A balanced model — neither false alarms nor misses dominate the error profile.

Try: The ticket classifier scores 86.

Confusion Matrix helper (accuracy, precision, recall, F1)

TP / FP / TN / FN -> Accuracy, Precision, Recall, F1

TP
True positives (count)
FP
False positives (count)
TN
True negatives (count)
FN
False negatives (count)
  • > 90 — Strong classifier
  • 70 - 90 — Usable classifier
  • < 70 — Weak classifier

Worked example

Support-ticket classifier over 1,000 tickets: TP 380, FP 60, TN 520, FN 40.

Accuracy 90.00% - Precision 86.36% - Recall 90.48% - F1 88.37%

Errors are split fairly evenly between false alarms and misses, so threshold tuning trades one for the other.

Try: Support-ticket classifier over 1,000 tickets: TP 380, FP 60, TN 520, FN 40.

Marketing & Sales

6 formulas

Customer Acquisition Cost (CAC)

CAC = Total sales and marketing spend / New customers acquired

S
Total sales and marketing spend in the period (USD)
N
New customers acquired in the same period (customers)
  • CAC payback < 12 months — Efficient
  • CAC payback 12-18 months — Acceptable
  • CAC payback > 18 months — Expensive

Worked example

A SaaS company spends $180,000 on sales and marketing in a quarter and signs 150 new customers.

CAC = 180,000 / 150 = 1,200

At $150 monthly revenue per customer, payback is 8 months — healthy if churn stays low.

Try: A SaaS company spends $180,000 on sales and marketing in a quarter and signs 150 new customers.

Customer Lifetime Value (LTV)

LTV = Average revenue per account x Gross margin % / Churn rate

ARPA
Average revenue per account per month (USD/month)
GM
Gross margin (ratio)
C
Monthly customer churn rate (ratio)
  • LTV > 3x CAC — Strong unit economics
  • LTV 1-3x CAC — Thin
  • LTV < CAC — Losing money per customer

Worked example

ARPA $150/month, gross margin 80%, monthly churn 2%.

LTV = 150 x 0.80 / 0.02 = 120 / 0.02 = 6,000

Average customer lifetime is 50 months; against $1,200 CAC the ratio is a healthy 5:1.

Try: ARPA $150/month, gross margin 80%, monthly churn 2%.

LTV:CAC Ratio

Ratio = LTV / CAC

LTV
Customer lifetime value (USD)
CAC
Customer acquisition cost (USD)
  • Ratio < 1 — Unsustainable
  • Ratio 1 - 3 — Below target
  • Ratio ≈ 3 — Healthy benchmark
  • Ratio > 5 — Under-investing

Worked example

LTV of $6,000 against CAC of $1,200.

Ratio = 6,000 / 1,200 = 5.0

Above the 3:1 benchmark — the company can increase acquisition spend to accelerate growth.

Try: LTV of $6,000 against CAC of $1,200.

Return on Ad Spend (ROAS)

ROAS = Revenue attributable to ads / Ad spend

R
Revenue attributed to the campaign (USD)
A
Ad spend for the campaign (USD)
  • ROAS < 1 — Losing money
  • ROAS 1 - 4 — Marginal to acceptable
  • ROAS >= 4 — Strong

Worked example

An e-commerce campaign spends $25,000 and drives $110,000 of attributed revenue at 45% gross margin.

ROAS = 110,000 / 25,000 = 4.4; break-even ROAS = 1 / 0.45 = 2.2

Double the break-even threshold — scale the campaign while ROAS stays above 2.2.

Try: An e-commerce campaign spends $25,000 and drives $110,000 of attributed revenue at 45% gross margin.

Conversion Rate

CR = (Conversions / Total visitors or leads) x 100

C
Conversions (purchases, signups, qualified leads) (conversions)
V
Visitors or leads entering the step (visits)
  • E-commerce > 3% — Above average
  • E-commerce 1-3% — Typical
  • E-commerce < 1% — Underperforming

Worked example

A landing page receives 24,000 sessions in a month and produces 660 signups.

CR = 660 / 24,000 x 100 = 2.75

A lift to 3.5% would add roughly 180 signups a month at zero extra ad spend.

Try: A landing page receives 24,000 sessions in a month and produces 660 signups.

Churn Rate

Churn % = (Customers lost in period / Customers at start of period) x 100

L
Customers lost during the period (customers)
S
Customers at the start of the period (customers)
  • < 1% monthly — Excellent
  • 1-3% monthly — Acceptable
  • > 5% monthly — Critical

Worked example

A subscription business starts the month with 3,200 customers and loses 64.

Churn = 64 / 3,200 x 100 = 2.0

Implies a 50-month average lifetime; cutting churn to 1% would double LTV.

Try: A subscription business starts the month with 3,200 customers and loses 64.

Strategy

5 formulas

Return on Investment

ROI = ((Gain - Cost) / Cost) x 100

Gain
Total benefit or return (USD)
Cost
Total investment cost (USD)
  • ROI > 20 — Strong return
  • 0 - 20 — Marginal return
  • ROI < 0 — Value destroying

Worked example

A CRM rollout costs $250,000 and is expected to generate $340,000 of margin over three years.

ROI = ((340,000 - 250,000) / 250,000) x 100 = 36%

A 36% cumulative return, but spread over three years — check the annualised figure before approving.

Try: A CRM rollout costs $250,000 and is expected to generate $340,000 of margin over three years.

Net Present Value (level annual cash flow)

NPV = -C0 + CF x [1 - (1 + r)^-n] / r

C0
Initial investment (USD)
CF
Annual net cash inflow (USD)
r
Discount rate (% per year)
n
Number of years (years)
  • NPV > 0 — Accept
  • NPV = 0 — Indifferent
  • NPV < 0 — Reject

Worked example

An automation programme costs $500,000 up front and saves $150,000 a year for five years. The corporate discount rate is 10%.

NPV = -500,000 + 150,000 x [1 - 1.1^-5] / 0.10 = -500,000 + 568,618

Positive NPV at a 10% hurdle rate — the programme creates roughly $69k of value in today money.

Try: An automation programme costs $500,000 up front and saves $150,000 a year for five years.

Internal Rate of Return (rate-guess method)

IRR = the rate r where NPV = 0

C0
Initial investment (USD)
CF
Annual net cash inflow (USD)
n
Number of years (years)
r
Guessed rate (% per year)
  • NPV > 100 — Guess too low
  • -100 to 100 — Close to IRR
  • NPV < -100 — Guess too high

Worked example

The same automation programme: $500,000 out, $150,000 a year for five years. Guessing 15%.

NPV at 15% = -500,000 + 150,000 x [1 - 1.15^-5] / 0.15 = +2,822; at 15.3% NPV is about zero

The IRR comfortably clears a 10% hurdle rate, confirming the positive NPV decision.

Try: The same automation programme: $500,000 out, $150,000 a year for five years.

Payback Period

Payback = Initial investment / Annual net cash inflow

C0
Initial investment (USD)
CF
Annual net cash inflow (USD per year)
  • < 2 — Fast payback
  • 2 - 4 — Typical payback
  • > 4 — Slow payback

Worked example

A warehouse automation cell costs $420,000 and cuts $140,000 of labour cost a year.

Payback = 420,000 / 140,000 = 3.0

Capital is recovered in three years; pair with NPV to judge the value created afterwards.

Try: A warehouse automation cell costs $420,000 and cuts $140,000 of labour cost a year.

Break-Even Point (units)

BEP = Fixed costs / (Price per unit - Variable cost per unit)

FC
Total fixed costs (USD)
P
Selling price per unit (USD)
VC
Variable cost per unit (USD)
  • > 0 — Break-even volume
  • < 0 — Invalid contribution

Worked example

A training business has $60,000 of fixed cost per cohort cycle, charges $1,200 per seat and incurs $450 of variable cost per seat.

BEP = 60,000 / (1,200 - 450) = 80

Eighty enrolments cover all costs; every seat beyond that contributes $750 of profit.

Try: A training business has $60,000 of fixed cost per cohort cycle, charges $1,200 per seat and incurs $450 of variable cost per seat.

Lean Six Sigma

8 formulas

Defects per Million Opportunities (DPMO)

DPMO = (Defects / (Units x Opportunities per Unit)) x 1,000,000

D
Number of defects found (defects)
U
Number of units inspected (units)
O
Defect opportunities per unit (opportunities)
  • DPMO <= 3.4 — 6 sigma
  • DPMO <= 233 — 5 sigma
  • DPMO <= 6210 — 4 sigma
  • DPMO <= 66807 — 3 sigma
  • DPMO <= 308538 — 2 sigma
  • DPMO <= 691462 — 1 sigma

Worked example

An invoicing team processes 1,500 invoices with 4 checkable fields each and finds 27 field errors.

DPMO = 27 / (1,500 x 4) x 1,000,000 = 27 / 6,000 x 1,000,000 = 4,500

Just above 4 sigma — solid, but a Green Belt project could realistically reach 5 sigma.

Try: An invoicing team processes 1,500 invoices with 4 checkable fields each and finds 27 field errors.

Defects per Unit (DPU)

DPU = Defects / Units

D
Number of defects (defects)
U
Number of units produced (units)
  • DPU < 0.01 — Excellent
  • DPU 0.01 - 0.10 — Acceptable
  • DPU > 0.10 — Poor

Worked example

A packaging line makes 2,400 cartons in a shift and QA logs 96 defects.

DPU = 96 / 2,400 = 0.04

4 defects per 100 cartons; combined with FTY this drives the rework cost estimate.

Try: A packaging line makes 2,400 cartons in a shift and QA logs 96 defects.

First Time Yield (FTY)

FTY = Units passed without rework / Units entering the step

Pass
Units passing the step first time (units)
In
Units entering the step (units)
  • FTY >= 0.99 — Excellent
  • FTY 0.95 - 0.99 — Acceptable
  • FTY < 0.95 — Poor

Worked example

A loan-application review receives 500 files; 465 pass first review, 35 go back for correction.

FTY = 465 / 500 = 0.93

7% rework at a single step; measure the other steps to get RTY before choosing where to improve.

Try: A loan-application review receives 500 files; 465 pass first review, 35 go back for correction.

Rolled Throughput Yield (RTY)

RTY = FTY1 x FTY2 x ... x FTYn

FTYn
First Time Yield of each process step (ratio)
n
Number of sequential steps (steps)
  • RTY >= 0.95 — Healthy end-to-end flow
  • RTY 0.80 - 0.95 — Watch the weakest step
  • RTY < 0.80 — Hidden factory

Worked example

Loan process with four steps at FTY 0.93, 0.97, 0.99 and 0.95.

RTY = 0.93 x 0.97 x 0.99 x 0.95 = 0.8484

Roughly 15 of every 100 applications are reworked somewhere — the 0.93 step is the priority.

Try: Loan process with four steps at FTY 0.

Process Capability (Cp)

Cp = (USL - LSL) / (6 x sigma)

USL
Upper Specification Limit (unit of measure)
LSL
Lower Specification Limit (unit of measure)
sigma
Process standard deviation (unit of measure)
  • Cp < 1.00 — Incapable
  • Cp 1.00 - 1.33 — Marginal
  • Cp >= 1.33 — Capable
  • Cp >= 2.00 — Six Sigma capable

Worked example

A machined shaft must be 20.00 ± 0.30 mm; the process standard deviation is 0.10 mm.

Cp = (20.30 - 19.70) / (6 x 0.10) = 0.60 / 0.60 = 1.00

Potentially capable but with zero margin — reduce variation to reach the 1.33 target.

Try: A machined shaft must be 20.

Process Capability Index (Cpk)

Cpk = min[(USL - mean) / (3 x sigma), (mean - LSL) / (3 x sigma)]

USL
Upper Specification Limit (unit of measure)
LSL
Lower Specification Limit (unit of measure)
mean
Process mean (unit of measure)
sigma
Process standard deviation (unit of measure)
  • Cpk < 1.00 — Not capable
  • Cpk 1.00 - 1.32 — Marginal
  • Cpk >= 1.33 — Capable
  • Cpk >= 1.67 — Highly capable

Worked example

Same shaft (USL 20.30, LSL 19.70, sigma 0.10) but the process is running at a mean of 20.10 mm.

Upper = (20.30 - 20.10) / 0.30 = 0.667; Lower = (20.10 - 19.70) / 0.30 = 1.333; Cpk = min = 0.667

Cp is 1.00 but Cpk is 0.67 — the process is off-centre by 0.10 mm. Re-centring alone triples the margin.

Try: Same shaft (USL 20.

Takt Time

Takt = Available production time / Customer demand

T
Available working time in the period (minutes)
D
Customer demand in the same period (units)
  • Cycle time < Takt — Capacity available
  • Cycle time = Takt — Perfectly balanced
  • Cycle time > Takt — Cannot meet demand

Worked example

A clinic runs an 8-hour day with two 15-minute breaks (450 productive minutes) and must see 60 patients.

Takt = 450 / 60 = 7.5

Any consultation step averaging over 7.5 minutes creates a queue — balance the line to that beat.

Try: A clinic runs an 8-hour day with two 15-minute breaks (450 productive minutes) and must see 60 patients.

Little's Law

Lead Time = Work in Process / Throughput (exit rate)

WIP
Work in process (items in the system) (items)
TH
Throughput / exit rate (items per day)
  • Lead time within customer promise — Flow is healthy
  • Lead time near the promise — Fragile
  • Lead time beyond the promise — Overloaded queue

Worked example

A support desk has 120 open tickets and closes 30 tickets per day.

Lead time = 120 / 30 = 4

To promise a 2-day response, cap open tickets at 60 or raise closure rate to 60 per day.

Try: A support desk has 120 open tickets and closes 30 tickets per day.