Percentage Calculator
A free online percentage calculator that handles the four questions people ask most often: What is X% of Y?, X is what percent of Y?, What is the percentage change from A to B?, and What is A increased or decreased by B%? Pick the tab that matches your question, enter two numbers, and get an instant, verified answer.
Choose a calculation
Choose a mode, enter two values, and press Calculate.
What a percentage actually means
A percentage is a fraction whose denominator is 100. Saying "15%" is shorthand
for the fraction 15 / 100, which is the same value as the decimal
0.15. This common denominator is what makes percentages so useful
for comparing quantities of different sizes: a 20% discount on a £30 item and a
20% discount on a £300 item are the same rate, even though the actual
savings differ.
The three relationships that cover almost every real-world percentage question are:
- Part = Whole × Rate. Finding X% of Y.
- Rate = Part ÷ Whole. Finding what percentage X is of Y.
- Change = (New − Old) ÷ Old. Finding percentage increase or decrease.
Formulas used by this calculator
1. X% of Y
result = Y × (X / 100)
Example: 15% of 200 = 200 × (15 / 100) = 30.
2. X is what % of Y
percent = (X / Y) × 100
Example: 45 is what percent of 180? (45 / 180) × 100 = 25%.
3. Percentage change from A to B
change = ((B − A) / |A|) × 100
A positive result is an increase, a negative result is a decrease. The absolute value in the denominator ensures the sign of the change describes the direction of movement, not the sign of the original number.
Example: from 80 to 100 → ((100 − 80) / 80) × 100 = 25% increase.
4. Increase or decrease a value by X%
increased = value × (1 + X / 100)
decreased = value × (1 − X / 100)
Example: 250 increased by 20% → 250 × 1.20 = 300. Decreased by
20% → 250 × 0.80 = 200.
Worked examples from everyday life
Tip on a restaurant bill
A bill is £84 and you want to leave an 18% tip. Use the "X% of Y" tab.
84 × (18 / 100) = 15.12. The tip is £15.12, and the total
comes to £99.12.
Tip = 15.12
Test score as a percentage
You answered 42 questions correctly out of 50. Use "X is what % of Y".
(42 / 50) × 100 = 84%.
Score = 84%
Price increase
A subscription rose from £12 to £15 per month. Use "Percentage change".
((15 − 12) / 12) × 100 = 25% increase.
Increase = 25%
Sale price
A jacket costs £140 and is on sale at 35% off. Use "Decrease by %".
140 × (1 − 0.35) = 91. The sale price is £91.
Sale price = 91
Common mistakes to avoid
- Confusing percentage points with percentages. If an interest rate rises from 4% to 6%, that is a 2 percentage-point rise but a 50% relative increase. Which one you need depends on the question being asked.
- Reversing the base. Going from 80 to 100 is a 25% increase, but going from 100 back to 80 is a 20% decrease — because the denominator changes. Percentage changes are not symmetric.
- Dividing by the new value in a change calculation. The formula always uses the original value as the denominator. Using the new value produces a different (and wrong) result.
-
Applying successive percentages by adding them.
A 10% discount followed by a further 20% discount is not a 30%
discount. It is
(1 − 0.10) × (1 − 0.20) = 0.72, i.e. a 28% discount overall.
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Frequently asked questions
Multiply the number by the percentage and divide by 100. For example, 15% of 200 = (200 × 15) / 100 = 30. In the calculator, use the "X% of Y" tab.
Percentage change = ((new − old) / |old|) × 100. A positive result is an increase, a negative result is a decrease. Use the "Percentage change" tab for this calculation.
Percentage change measures a change from an original value to a new value and uses the original as the denominator. Percentage difference compares two values symmetrically and uses their average as the denominator, so the result is the same regardless of which value you enter first.
Yes. The percent change tab accepts negative values on either side and uses the absolute value of the original for the denominator, so the direction of change is reported correctly.
To add X% to a value, multiply it by (1 + X / 100). To remove X% from a value, multiply it by (1 − X / 100). Use the "Increase / decrease by %" tab.