Basic
What is X% of Y?
What is of ?
Working: 80 × 15 ÷ 100 = 12
X is what percent of Y?
is what percent of ?
Working: 12 ÷ 80 × 100 = 15%
X is Y% of what?
Works backwards from a part to the whole.
is of what?
Working: 12 × 100 ÷ 15 = 80
Increase a number by a percentage
Increase by
Working: 80 × (1 + 15 ÷ 100) = 92
- Amount added
- 12
Decrease a number by a percentage
Decrease by
Working: 80 × (1 − 15 ÷ 100) = 68
- Amount taken off
- 12
Change
Percent change
How much a value went up or down, as a percentage of where it started. A rise shows as +, a fall as −.
From to
Working: (65 − 50) ÷ 50 × 100 = +30%
- Difference
- +15
Percent difference
For two values where neither is the “before”, like two quotes for the same job. It divides the gap by their average, so swapping them gives the same answer. Percent change is different: it depends on which value came first.
Between and
Working: |50 − 65| ÷ ((50 + 65) ÷ 2) × 100 = 26.087%
- Average
- 57.5
Percentage points vs percent
When the numbers are themselves percentages, the plain gap between them is in percentage points. An interest rate going from 4% to 5% is up 1 percentage point, but up 25% compared with what it was. Both are right; they answer different questions.
A rate goes from to
Working: 5 − 4 = 1 point
- Relative change
- (5 − 4) ÷ 4 × 100 = +25%
Reverse & tax
Original value before a percentage change
For questions like “the price after 20% off is 64, what was it?”. This divides; subtracting or adding the percentage gives the wrong answer.
After a , it's . What was it before?
Working: 64 ÷ (1 − 20 ÷ 100) = 80
- The decrease was
- 16
Not 76.8: the 20% was worked out on the original, not on 64.
Add or remove tax or VAT
Remove takes the tax out of a price that already includes it.
tax at on
Working: 100 × (1 + 20 ÷ 100) = 120
- Tax
- 20
- Before tax
- 100
Money
Discount and sale price
off
Working: 80 × (1 − 25 ÷ 100) = 60
- You save
- 20
Stacked discounts
Each discount comes off the price left after the one before. Leave any you don't need empty.
with off, then off, then off
Working: 100 × (1 − 20 ÷ 100) × (1 − 10 ÷ 100) = 72
- You save
- 28
- Total discount
- 28%
Not 30%: each discount comes off the already-reduced price.
Margin and markup from cost and price
Markup is profit as a percentage of the cost. Margin is profit as a percentage of the selling price.
Cost , selling price
Working: (100 − 60) ÷ 100 × 100 = 40%
- Profit
- 40
- Markup
- (100 − 60) ÷ 60 × 100 = 66.6667%
Price for a target margin or markup
Cost , aiming for a
Working: 60 ÷ (1 − 40 ÷ 100) = 100
- Profit
- 40
Convert margin to markup, or back
A
Working: 40 ÷ (100 − 40) × 100 = 66.6667%
Tips and bill splitting are on tip.gripe; loan and mortgage interest on loans.gripe.
Converters
Fraction, decimal and percent
Type in any box and the other two follow. Fractions can be mixed numbers, like 1 1/2.
Working: 3/8 = 0.375 × 100 = 37.5%
Ratio to percent
Each side's share of the whole. A 3 : 1 mix is 75% and 25%.
Ratio :
Working: 3 ÷ 4 × 100 = 75%
- Second part
- 1 ÷ 4 × 100 = 25%
- First as a % of the second
- 3 ÷ 1 × 100 = 300%
Grade percentage
out of
Working: 42 ÷ 50 × 100 = 84%
- Points missed
- 8
Compound
Repeated percentage change
Each period's change applies to the result of the one before. Use a minus sign for a fall, like −5.
Start at , change by each period, for periods
Working: 100 × (1 + 5 ÷ 100)^10 = 162.8895
- Change
- +62.8895
Not 50%: each period's change applies to the value left by the one before.
CAGR (compound annual growth rate)
The steady yearly rate that gets from the first value to the second. Years can be fractional: 18 months is 1.5.
From to over years
Working: (200 ÷ 100)^(1 ÷ 5) − 1 = 14.8698%
About these calculators
How do I check the answer?
Every answer has its sum written underneath, so you can redo it on paper. “What is 15% of 80” is 80 × 15 ÷ 100 = 12.
Percent change or percent difference?
Change has a direction. From 50 to 65 is up 30%, and from 65 back to 50 is down 23.08%. Difference has no before and after: it compares the gap with the average of the two numbers, so 50 and 65 are 26.09% apart whichever way round you put them.
What's a percentage point?
The plain gap between two percentages. A rate going from 4% to 5% is up one percentage point, which is a 25% rise in the rate. Both statements are true and they get mixed up a lot.
Why doesn't 20% up then 20% down get me back?
The second 20% is taken from a bigger number. 100 plus 20% is 120, and 20% off 120 is 96. It's also why finding the price before a discount means dividing: 64 after 20% off was 64 ÷ 0.8 = 80.
Margin or markup?
Both are profit as a percentage, of different things. Markup is profit over cost, margin is profit over the selling price. Buy at 60 and sell at 100, and that's a 66.67% markup but a 40% margin.
How do I type numbers?
15, 15% and 1,234.5 all work. If your device writes decimals with a comma, 12,5 is read as twelve and a half. Choose how many decimal places to show at the top of the page.
Is anything sent anywhere?
No. The sums are done in your browser. The last numbers you typed are kept on this device, and the address bar holds the sum you're on, so you can bookmark or share it.
Nothing is sent anywhere.