Percentages for design and the shop floor
Yield, fill, achievement, plus-minus tolerance, tax in and out, year-over-year, and percentage points. Turn a report or floor figure into a percentage on the spot — and recall which definition you are using.
What share one number is of another. The chips switch what ÷ what, so the definition under the result matches the sheet you are filling.
Nominal, plus, and minus — then the limits. A measured value is optional; it shows where you sit in the band.
Percentage change between two values. The index (new ÷ old) sits beside it — that is the year-over-year 125 percent on many ops reports.
Exclusive, tax, and inclusive. The trap is multiplying the inclusive amount by the rate — that is not the tax.
The gap between two percentages, and the relative change of that gap.
The picture follows the numbers.
What the numbers mean
Share and achievement
part ÷ whole × 100
Achievement is actual ÷ target. Yield is good ÷ started. Fill is contents ÷ capacity. They look the same as arithmetic and differ in the labels.
Tolerance
upper = nominal + plus; lower = nominal + minus
The allowed band on the drawing. A measured value is a point in that band, or outside it — not the tolerance itself.
Change vs last period
((new − old) ÷ old) × 100
From 120 to 150 is +25 percent. The index (new ÷ old) is 125 percent. A report that prints year-over-year 125 percent usually means the index.
Tax in and out
tax = exclusive × rate; exclusive = inclusive ÷ (1 + rate)
Do not multiply the inclusive amount by the rate. That figure is not the tax.
Percentage points
points = new percent − old percent; change = points ÷ old percent
8 percent to 10 percent is 2 points, and a 25 percent relative rise. A line that says up 2 percent may mean either.
Tips
Percent and Percentage Points Are Not the Same
A rate moving from 8% to 10% is two percentage points. Relative to 8%, that is a 25% rise. A line that says "up 2%" may mean either; the two numbers answer different questions.
Year-Over-Year 125% Is Not +125%
Change is (new − old) ÷ old. From 120 to 150 that is +25%. The index — new ÷ old — is 125%. A monthly report that says year-over-year 125% is usually the index, not a 125% jump.
Operating Rate and Availability Split on the Denominator
Operating rate divides running time by calendar or loaded time — the sheet at your plant decides which. Availability divides running time by time the machine could run, after downtime you already took out. They are not interchangeable.
A Tolerance Is an Allowed Band, Not the Error You Measured
Upper = nominal + plus, lower = nominal + minus (the minus is often a negative number). The reading sits somewhere in that band, or outside it. Precision and resolution are different questions.
Common Use Cases
Achievement Against a Target
84 against a plan of 100 is 84% achievement — actual ÷ target, not a slice of a total.
Yield and Defect Rate
970 good pieces from 1,000 started is 97% yield. The defect rate is scrap ÷ started. Rework means the two need not add to 100%.
Fill on a Drawing or a Hopper
850 into a 1,000 capacity is 85% fill. Whether the denominator is bulk, void, or board area comes from the drawing, not from yield.
Limits on a Dimension
Nominal 20, plus 0.10, minus 0.05 → 20.10 / 19.95. A measured 20.04 sits inside that band.
Tax-Exclusive and Tax-Inclusive
On a 10 percent invoice, $10,000 exclusive is $11,000 inclusive. Inclusive ÷ 1.10 is exclusive. Multiplying the inclusive amount by the rate is not the tax.
This Period Versus Last
Output 1,200 last month and 1,500 this month is +25% change, and 125% as an index — the pair that belongs in the monthly note.