Percentage Calculator

How Percentages Work — Practical Guide

A percentage is a ratio expressed as a fraction of 100. The word comes from the Latin per centum — "by the hundred." Percentages are used everywhere: discounts, tax rates, interest rates, exam scores, statistical data, and financial returns all use percentage notation because it provides a consistent, comparable scale regardless of the underlying quantities.

The Four Core Percentage Problems

Question	Formula	Example
What is X% of Y?	Result = (X ÷ 100) × Y	15% of £80 = £12
X is what % of Y?	Result = (X ÷ Y) × 100	30 is 60% of 50
% increase from X to Y	((Y − X) ÷ X) × 100	50→65 = 30% increase
% decrease from X to Y	((X − Y) ÷ X) × 100	100→75 = 25% decrease

Common Real-World Uses

Retail discounts: A 30% discount on a £120 item = £120 × 0.30 = £36 off. Sale price = £84.
VAT / Sales tax: Adding 20% VAT to £50: £50 × 1.20 = £60. Removing VAT from £60: £60 ÷ 1.20 = £50.
Exam scores: 72 correct out of 90 questions = (72 ÷ 90) × 100 = 80%.
Investment returns: Portfolio grew from £8,000 to £9,200. Return = ((9,200 − 8,000) ÷ 8,000) × 100 = 15%.
Tip calculation: 18% tip on a £45 meal = £45 × 0.18 = £8.10 tip. Total = £53.10.

Percentage Points vs Percentages — An Important Distinction

A change from 20% to 25% is a 5 percentage point increase, but a 25% relative increase. This distinction matters in finance and statistics: if a central bank raises rates from 2% to 3%, that is a 1 percentage point increase (or a 50% increase relative to the original rate). Always check whether a reported change is in percentage points or relative percent.

The Three Types of Percentage Problems

Type 1: What is X% of Y?

Multiply Y by (X ÷ 100). Example: 15% of £80 = 80 × 0.15 = £12.

Type 2: X is what percentage of Y?

Divide X by Y × 100. Example: 35 is what % of 140? = (35 ÷ 140) × 100 = 25%.

Type 3: Percentage Change

Change = [(New − Old) ÷ Old] × 100. Increase: $50 → $65 = +30%. Decrease: $200,000 → $160,000 = −20%.

Key Percentage Formulas

Increase by X%: New = Original × (1 + X/100)
Decrease by X%: New = Original × (1 − X/100)
Reverse an increase: Original = New ÷ (1 + X/100)

Percentages in Everyday Life

Shopping: 20% off £75 = £75 × 0.8 = £60
Restaurant tip: 18% on $55 = $9.90
VAT: 20% on £120 net = £120 × 1.2 = £144
Exam score: 68 out of 85 = (68÷85)×100 = 80%
Weight loss: 4 kg lost from 85 kg = 4.7%

Common Percentage Mistakes

Percentages are not symmetrical: +50% then −50% does NOT return to start. 100 → 150 → 75.
Reversing a discount: If price is £90 after 10% off, original = £90 ÷ 0.9 = £100 (not £90 + 10%).
Percentage point vs percentage: Rate rising from 2% to 3% is a 1 percentage-point increase but a 50% relative increase.

Related Tools

Tax Calculator — income tax percentages across all brackets. Tip Calculator — split any tip percentage instantly.

Worked example — discount: A £120 jacket is on sale with 35% off. Discount = 35% of £120 = 0.35 × 120 = £42. Sale price = £120 − £42 = £78. If VAT at 20% is added at the till, final price = £78 × 1.20 = £93.60. The percentage calculator handles this step by step — use the "X% of Y" mode for the discount, then the "add percentage" mode for the VAT.

Percentages are everywhere — shopping discounts, tax rates, investment returns, exam results, and statistical reports all rely on the same hundred-based ratio. The percentage calculator handles each of these scenarios in a dedicated mode so you never have to wonder which formula to apply.

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How to Use

1
Select calculation typeChoose from: "What is X% of Y?", "X is what % of Y?", or "% change from X to Y".
2
Enter your numbersType the values into the input fields provided for your chosen calculation type.
3
Get instant resultThe answer appears immediately as you type, with the formula shown so you can verify the working.

Frequently Asked Questions

How do I calculate 15% of a number?

Multiply the number by 0.15. For example, 15% of 80 = 80 × 0.15 = 12. Alternatively, divide the number by 100 and multiply by 15.

What is the formula for percentage change?

Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. A positive result means an increase; a negative result means a decrease.

How do I find what percentage one number is of another?

Divide the first number by the second number, then multiply by 100. Example: what percentage is 45 of 180? (45 ÷ 180) × 100 = 25%.

What is the difference between percentage and percentage points?

A percentage is relative to a base value (e.g., 10% of 200 = 20). A percentage point is an absolute difference between two percentages. If interest rates go from 3% to 5%, that is a 2 percentage point increase, but a 66.7% relative increase.

How do I add a percentage to a number?

To add X% to a number, multiply the number by (1 + X/100). For example, to add 20% to $50: $50 × 1.20 = $60. To subtract X%, multiply by (1 − X/100).

How do I calculate the percentage change between two numbers?

Subtract the original value from the new value, divide the result by the original value, and multiply by 100. If the result is positive it is a percentage increase; if negative it is a decrease. Example: a salary rises from $50,000 to $55,000. Change = ((55,000 - 50,000) ÷ 50,000) × 100 = (5,000 ÷ 50,000) × 100 = 10% increase. The percentage calculator has a dedicated mode for this so you do not need to memorise the formula.