％ Percentage

Percentage Calculator

Four of the most common percentage questions in one page — pick a mode, fill in the two numbers and press Calculate.

Written and reviewed by SM Arijul Islam · Last reviewed 20 October 2026 · Editorial standards · Report an error

Percentage formulas

X% of Y = X ÷ 100 × Y
X is what percent of Y = X ÷ Y × 100
Percentage change = (Y − X) ÷ |X| × 100
Percentage difference = |X − Y| ÷ ((X + Y) ÷ 2) × 100
Add X% = Y × (1 + X ÷ 100) · Subtract X% = Y × (1 − X ÷ 100)

Percentage change vs percentage difference

Percentage change compares a new value against an original baseline, so the direction matters. Percentage difference compares two values of equal standing without a baseline, which is why the result is always positive.

A 20% discount followed by a 20% increase does not return you to the original price — you end up 4% lower.

Worked example

15% of 240 is 36. Turned around, 36 is 15% of 240. Going from 240 to 300 is a 25% increase, while going back from 300 to 240 is a 20% decrease — the same change, described from different directions.

Percentage of a value = (part ÷ whole) × 100. Percentage change = (new − old) ÷ old × 100.

Everyday uses

Discounts, tips and sale prices
Tax and VAT calculations
Exam marks and grade boundaries
Growth rates in reports and dashboards
Comparing survey or test results

Frequently asked questions

What is the difference between percentage change and percentage difference?

Percentage change compares a new value with an earlier one; percentage difference compares two values with their average, with no direction.

How do I work out a percentage increase?

Divide the increase by the original value and multiply by 100.

Why doesn't a 50% fall reverse with a 50% rise?

Because the rise applies to a smaller base. A fall from 100 to 50 needs a 100% rise to get back to 100.

What is a percentage point?

The simple arithmetic difference between two percentages. Going from 5% to 7% is a 2-point rise but a 40% relative increase.

More worked examples

15% of 240 is 36, and 36 is 15% of 240 — the same relationship seen from either side.
A 120 item with 25% off costs 90, a saving of 30.
Going from 80 to 100 is a 25% increase, but going back from 100 to 80 is only a 20% decrease.
A price that rises 10% and then falls 10% ends up 1% lower: 100 becomes 110, which falls to 99.

Common fractions and percentages

Common fractions expressed as percentages
Fraction	Percentage
1/8	12.5%
1/5	20%
1/4	25%
1/3	33.33%
1/2	50%
2/3	66.67%
3/4	75%

Common mistakes to avoid

Adding percentage changes together. A 10% rise followed by a 10% fall is a 1% net fall, not zero.
Confusing percentage points with percentages. Moving from 5% to 7% is a 2-point rise but a 40% increase.
Taking a percentage of the wrong base — discounts apply to the original price, not the already-discounted one.
Assuming a fall and an equal rise cancel out, when in fact the rise applies to a smaller number.

Further questions

How do I find the original price after a discount?

Divide the discounted price by (1 minus the discount). A 90 price after 25% off means 90 ÷ 0.75 = 120.

What is the difference between markup and margin?

Markup is measured against cost; margin is measured against the selling price. The same profit is a different percentage in each.

How do I calculate a weighted average percentage?

Multiply each percentage by its weight, add the results, then divide by the total weight.

Why is a third not exactly 33%?

Because 1/3 is 33.333…%. Rounding to 33% leaves a small error that grows when you multiply by large numbers.

Percent off, percentage change and common questions

What is 20 percent of 50 is 10, because 50 × 0.20 = 10. 30 percent off 80 is 56, because 80 × 0.30 = 24 and 80 − 24 = 56. For how do I calculate percentage change, divide the difference by the original and multiply by 100: from 80 to 100 is (20 ÷ 80) × 100 = a 25% increase.

Common percentage questions worked out
Question	Method	Answer
20% of 50	50 × 0.20	10
30% off 80	80 − (80 × 0.30)	56
15% of 200	200 × 0.15	30
Change from 80 to 100	(100 − 80) ÷ 80 × 100	+25%
Change from 100 to 80	(80 − 100) ÷ 100 × 100	−20%

Note that a 20% fall is not undone by a 25% rise on the smaller number — the base changes, which is the most common percentage mistake in pricing and pay negotiations.