Maths

How do you calculate percentage increase?

One formula, three mistakes that people make with it, and the reason percentage changes do not cancel out.

Percentage increase = (New value − Old value) ÷ Old value × 100. If a price rises from 200 to 250, the increase is (250 − 200) ÷ 200 × 100 = 25%. The critical detail is that you divide by the old value, never the new one — dividing by 250 instead would give 20%, which is the answer to a different question.

Worked out 2026-09-04 (IST) · Percentage change measured against the original value

Worked examples

Percentage increase, step by step
Old value	New value	Difference	Divided by old	Percentage change
200	250	+50	0.2500	+25.0%
50	75	+25	0.5000	+50.0%
1200	1500	+300	0.2500	+25.0%
80	60	-20	-0.2500	-25.0%
2500	2000	-500	-0.2000	-20.0%
45000	52000	+7000	0.1556	+15.6%

The three variants you actually need

Percentage formulas
You want	Formula	Example
Percentage increase	(New − Old) ÷ Old × 100	200 → 250 = +25%
Percentage decrease	(Old − New) ÷ Old × 100	250 → 200 = −20%
A percentage of a number	Number × percent ÷ 100	15% of 4,000 = 600
Increase a number by a percentage	Number × (1 + percent ÷ 100)	4,000 + 15% = 4,600
Reverse a percentage increase	New ÷ (1 + percent ÷ 100)	590 before 18% GST = 500
Percentage difference between two values	\|A − B\| ÷ ((A+B) ÷ 2) × 100	200 vs 250 = 22.2%

Why gains and losses are not symmetric

The gain needed to recover a loss
Loss	Gain needed to break even
−10%	+11.1%
−20%	+25.0%
−30%	+42.9%
−50%	+100.0%
−70%	+233.3%
−90%	+900.0%

The mistake to watch for. Averaging percentage changes across periods gives the wrong answer, because each period compounds on the last. +10% then −10% is not 0%, it is −1%. For multi-period growth use the compound annual growth rate: (End ÷ Start)^1/n − 1.

Check your own numbers

Percentage of, percentage change, percentage difference and reverse percentage, all in one place.

Percentage CalculatorPercentage of a number, percentage change, increase, decrease and reverse percentage.

Frequently asked

What is the formula for percentage decrease?

The same formula — (New minus Old) divided by Old, times 100 — which simply returns a negative number when the value falls. If you prefer a positive answer, use (Old minus New) divided by Old times 100. A fall from 250 to 200 is a 20% decrease, even though the rise from 200 to 250 was a 25% increase, because the base is different each time.

Why does a 50% rise then a 50% fall not return to the start?

Because the second percentage is applied to a bigger number. 100 rises 50% to 150; 150 then falls 50% to 75, not 100. To reverse a 50% rise you need a 33.3% fall. This asymmetry is why investment losses hurt more than equivalent gains help: a 50% loss needs a 100% gain to break even.

How do I find the original value after a percentage increase?

Divide, do not subtract. If a price is 590 after an 18% GST increase, the original is 590 divided by 1.18 = 500. Subtracting 18% of 590 would give 483.80, which is wrong. The rule is Original = New divided by (1 + increase as a decimal).

What is the difference between percentage points and percent?

A move from 5% to 7% is a rise of 2 percentage points but a 40% increase. News reports mix these constantly, especially for interest rates and vote shares. Use "percentage points" for the arithmetic difference between two percentages and "percent" for the relative change between two values.

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