How to Calculate Percentages

Use the How to Calculate Percentages

A percentage is a number out of 100. To find a percentage of a number, multiply the number by the percentage, then divide by 100.

The simplest formula

X% of Y = Y × X ÷ 100. For example, 20% of 150 is 150 × 20 ÷ 100 = 30.

Most everyday percentage questions are just variations of this idea: finding a part, comparing two numbers, or increasing/decreasing a value.

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Use the calculator for percentage of, percentage change, percentage difference, add percentage and subtract percentage.

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What a percentage actually means

Percent means “per hundred”. So 25% means 25 out of 100, 50% means half, and 100% means the whole amount.

Percentage	Fraction	Decimal	Plain-English meaning
10%	1/10	0.10	Ten out of every hundred
25%	1/4	0.25	One quarter
50%	1/2	0.50	Half
75%	3/4	0.75	Three quarters
100%	1 whole	1.00	The full amount

When a calculator asks for a percentage, it usually converts that percentage into a decimal behind the scenes. For example, 20% becomes 0.20.

How to calculate a percentage of a number

This is the most common percentage calculation. You use it when you want to know things like 15% of a bill, 20% VAT on a net price, or 30% of a total.

Percentage of a number = number × percentage ÷ 100

Example:
20% of 150 = 150 × 20 ÷ 100 = 30

For money values, round the final answer to 2 decimal places. Do the calculation first, then round at the end.

How to find what percentage one number is of another

Use this when you know the part and the total, but you want the percentage. For example, if 30 people out of 150 answered yes, what percentage answered yes?

Percentage = part ÷ whole × 100

Example:
30 ÷ 150 × 100 = 20%

Watch the order: the smaller number is not always the part. The formula depends on what you are comparing with what.

How to calculate percentage increase or decrease

Percentage change compares a new value with an old starting value. This is useful for price rises, pay rises, bill increases, savings drops and growth figures.

Percentage change = (new value − old value) ÷ old value × 100

Example increase:
Old value £100, new value £125
(125 − 100) ÷ 100 × 100 = 25% increase

Example decrease:
Old value £125, new value £100
(100 − 125) ÷ 125 × 100 = -20%, so this is a 20% decrease

The starting value matters. Going from £100 to £125 is a 25% increase, but going from £125 back to £100 is only a 20% decrease because the starting number is different.

For pay examples, the pay rise calculator can help convert a salary change into a percentage and yearly/monthly difference.

Percentage increase vs percentage difference

Percentage increase or decrease needs a clear old value and new value. Percentage difference compares two numbers against their average, so it is better when neither number is the obvious starting point.

Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100

Example:
A = 100 and B = 125
Difference = 25
Average = 112.5
25 ÷ 112.5 × 100 = 22.22%

A percentage point is different again. If a rate moves from 20% to 25%, it has gone up by 5 percentage points, but the percentage increase is 25%.

Need the difference between two figures?

The percentage calculator includes a percentage difference mode so you do not have to choose the wrong formula.

Calculate percentage difference

How to add or subtract a percentage

Adding or subtracting a percentage is common for price rises, discounts, VAT, service charges and savings.

Task	Formula	Example
Add 20%	Value × 1.20	£100 × 1.20 = £120
Add 5%	Value × 1.05	£200 × 1.05 = £210
Subtract 20%	Value × 0.80	£100 × 0.80 = £80
Subtract 15%	Value × 0.85	£60 × 0.85 = £51

VAT warning: removing VAT from a VAT-inclusive price is not the same as subtracting the VAT rate. At 20%, you divide by 1.20. Use the VAT calculator for that calculation.

Worked examples

Discount£80 with 25% off: £80 × 25 ÷ 100 = £20 saving, so the sale price is £60.

Tip£45 bill with a 10% tip: £45 × 10 ÷ 100 = £4.50 tip, so the total is £49.50.

Price rise£120 to £138: (138 − 120) ÷ 120 × 100 = 15% increase.

Unit price£3 for 500g means £3 ÷ 500 = £0.006 per gram, or 60p per 100g.

For shopping examples, the discount calculator and unit price comparison calculator are usually quicker than doing the maths manually.

Common percentage mistakes

Using the wrong starting valueA percentage increase depends on the old value. A percentage decrease depends on the starting value before the decrease.

Confusing percent and percentage points20% to 25% is a 5 percentage-point rise, not a 5% rise.

Removing VAT incorrectlyTo remove 20% VAT from a gross price, divide by 1.20. Do not just subtract 20%.

Rounding too earlyFor money, calculate first and round the final answer to 2 decimal places.

FAQs

How do I calculate 20% of a number?

Multiply the number by 20, then divide by 100. You can also multiply by 0.20.

How do I calculate percentage increase?

Subtract the old value from the new value, divide the result by the old value, then multiply by 100.

What is the difference between percentage change and percentage difference?

Percentage change compares a new value with an old starting value. Percentage difference compares two values against their average.

How do I subtract a percentage?

Convert the percentage into a decimal and subtract it from 1. For example, subtracting 20% means multiplying by 0.80.

Why is removing VAT different from subtracting 20%?

Because the VAT-inclusive price already contains VAT. At 20%, the net price is the gross price divided by 1.20, and the VAT is the difference between the two.