Percentage Calculator

A percentage expresses a number as a fraction of 100. The word comes from the Latin “per centum”, meaning “by the hundred.”

The four formulas behind the tabs above:

1. Find a percentage of a number: Result = (Percentage / 100) × Number

2. Find what percentage A is of B: Percentage = (A / B) × 100

3. Find the original number when you know a percentage: Original = Result / (Percentage / 100)

4. Find the change between two values: Change = ((New − Old) / |Old|) × 100

Worked examples:

Example 1, what is 35% of 240? Result = (35 / 100) × 240 = 84

Example 2, what percentage is 45 of 180? Percentage = (45 / 180) × 100 = 25%

Example 3, 60 is 15% of what number? Original = 60 / (15 / 100) = 60 / 0.15 = 400

Example 4, a price goes from 80 to 100. Change = ((100 − 80) / 80) × 100 = 25% increase. Going back the other way is a 20% decrease, not 25%, because the two are measured against different starting points. That asymmetry is the single most common percentage mistake there is.

Common uses:

• Discounts: a 20% off sale on a £150 item saves £30
• Tax: 20% VAT on £80 adds £16
• Test scores: getting 42 out of 56 questions right = 75%
• Interest rates: 5% annual interest on £10,000 = £500/year
• Tip calculation: 15% tip on a £65 bill = £9.75

Percentage vs percentage points: These are different. If interest rates rise from 2% to 3%, that is a 1 percentage point increase, but a 50% increase in the rate itself. This distinction matters in finance and statistics.

Quick mental maths tricks:

• 10% = move decimal one place left (£250 → £25)
• 5% = half of 10%
• 1% = divide by 100
• 25% = divide by 4
• 33% ≈ divide by 3