How to Calculate a Percentage: The Complete Guide

Percentages are everywhere — pay rises, tax rates, sale discounts, exam results. And yet the moment someone asks "what's 17.5% of £340?" most people reach for their phone. Understanding how percentages actually work means you can check any calculation yourself, catch errors quickly and make better decisions on the fly.

This guide covers the core percentage formula, the most common types of percentage calculation, and a few mental shortcuts that make quick estimates much easier.

The Basic Percentage Formula

Every percentage calculation comes back to one underlying idea: a percentage is a fraction of 100. The word itself comes from the Latin per centum, meaning "per hundred". So 40% simply means 40 out of every 100, or the fraction 40/100, which simplifies to 0.40 as a decimal.

The core formula for finding what percentage one number is of another is:

So if you scored 36 out of 45 on a test, your percentage score is (36 ÷ 45) × 100 = 80%.

How to Find X% of a Number

This is the most common percentage calculation. The formula is:

In practice, you just convert the percentage to a decimal and multiply. To find 15% of 200, convert 15% to 0.15 and multiply: 200 × 0.15 = 30.

This formula applies to almost anything: calculating a tip on a restaurant bill, working out VAT on a purchase, finding a commission amount, or splitting a percentage of your salary into savings.

How to Find What Percentage One Number Is of Another

Flip the calculation around and you get the second core formula:

If you scored 54 marks out of 60 on an exam, your percentage is (54 ÷ 60) × 100 = 90%. If your team won 14 of 20 games, your win rate is (14 ÷ 20) × 100 = 70%.

How to Add or Subtract a Percentage

Adding a percentage — for a tip, a tax or a markup — uses this formula:

To add 20% VAT to a price of £80: 80 × 1.20 = £96. The "1 +" part preserves the original amount, and the 0.20 adds the 20%.

To subtract a percentage — for a discount — you replace the "+" with "−":

A 25% discount on a £120 item: 120 × 0.75 = £90.

Quick Mental Shortcuts

You don't always need a calculator. A few reliable shortcuts cover most situations:

• 10%: move the decimal point one place to the left. 10% of 350 = 35.
• 1%: move the decimal point two places to the left. 1% of 350 = 3.5.
• 5%: find 10% and halve it. 5% of 350 = 17.5.
• 20%: find 10% and double it. 20% of 350 = 70.
• 15%: find 10%, find 5%, add them. 15% of 350 = 35 + 17.5 = 52.5.
• 50%: divide by 2.
• 25%: divide by 4.

These shortcuts are fast enough for tips, quick checks and rough estimates. For exact answers, the calculator below handles everything automatically.

The Most Common Percentage Mistakes

Using the wrong denominator. When calculating percentage change — say a price rising from £80 to £100 — you always divide by the original value, not the new one. The correct answer is (20 ÷ 80) × 100 = 25%. Using 100 as the denominator instead would give 20%, which is wrong.

Confusing percentage points with percent. If a tax rate rises from 20% to 25%, it has risen by 5 percentage points. But it has risen by 25% in relative terms (5 ÷ 20 × 100). These are different measures that frequently get mixed up in news reporting and financial documents.

Assuming increases and decreases cancel out. A 50% increase followed by a 50% decrease doesn't return to the starting value. Start with 100: a 50% increase gives 150, then a 50% decrease gives 75. The two percentages are applied to different base numbers, so they don't cancel symmetrically.

Recap: The Four Core Formulas

• Find X% of Y: Y × (X ÷ 100)
• What % is A of B? (A ÷ B) × 100
• Add X% to Y: Y × (1 + X ÷ 100)
• Subtract X% from Y: Y × (1 − X ÷ 100)

Once you're comfortable with these four, every other percentage problem is just a variation. Percentage change, reverse percentages and percentage difference all follow the same logic — they just rearrange which numbers you know and which you're solving for.

This article is for general educational purposes. Results should be verified with a calculator for financial, tax or exam-related decisions.