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How to Calculate Percentage: The Seven Cases You Actually Need

How to calculate percentage in seven everyday cases: percent of a number, increase, decrease, reverse percentages and more, with worked examples.

By Vigneshwaran M · 2026-10-03 · 5 min read

Note: This article was written with AI assistance and may contain inaccuracies or outdated information. Please check important details against the official sources listed below.

A percentage is just a fraction out of 100. "Fifteen percent" means 15 out of every 100, or 0.15. Almost every percentage question you meet in daily life fits one of seven patterns, and once you recognise the pattern the arithmetic is two steps. This guide walks through each with its own numbers. You can confirm any answer with the percentage calculator.

The one idea behind everything: to convert a percentage to a decimal, divide by 100. To convert a decimal back, multiply by 100.

The seven cases

Case 1: Find a percentage of a number

Formula: part = whole × percent ÷ 100

Example: what is 15% of 840?

  • 840 × 15 = 12,600
  • 12,600 ÷ 100 = 126

So 15% of 840 is 126. A mental shortcut: 10% of 840 is 84, 5% is half of that (42), and 84 + 42 = 126.

Case 2: What percentage is one number of another?

Formula: percent = part ÷ whole × 100

Example: 45 marks out of 180. What percentage is that?

  • 45 ÷ 180 = 0.25
  • 0.25 × 100 = 25%

The "whole" is always the thing you are comparing against, the number after "out of" or "of".

Case 3: Find the whole when you know the part

Formula: whole = part × 100 ÷ percent

Example: 36 is 12% of some number. What is the number?

  • 36 × 100 = 3,600
  • 3,600 ÷ 12 = 300

Check by going forward: 12% of 300 = 300 × 12 ÷ 100 = 36. Correct.

Case 4: Percentage increase

Formula: increase % = (new − old) ÷ old × 100

Example: a value goes from 80 to 92.

  • Change = 92 − 80 = 12
  • 12 ÷ 80 = 0.15
  • 0.15 × 100 = 15%

The base is the old value, because the question is "how much did it grow compared with where it started?"

Case 5: Percentage decrease

Formula: decrease % = (old − new) ÷ old × 100

Example: a value drops from 250 to 200.

  • Change = 250 − 200 = 50
  • 50 ÷ 250 = 0.2
  • 0.2 × 100 = 20%

Notice that the base is still the old value. Going back from 200 to 250 is an increase of 50 ÷ 200 = 25%, which is not the same as 20%. Increases and decreases between the same two numbers are different percentages because their bases differ.

Case 6: Apply a percentage increase or decrease

Multiply by a factor instead of working out the change separately.

  • Increase by p%: multiply by 1 + p ÷ 100
  • Decrease by p%: multiply by 1 − p ÷ 100

Example: start with 640.

  • Increase by 15%: 640 × 1.15 = 736
  • Decrease by 15%: 640 × 0.85 = 544

Check the first one the long way: 15% of 640 = 96, and 640 + 96 = 736. Correct.

Case 7: Work back to the original value

You know the value after a change and the percentage of that change. Divide by the factor from case 6.

Example: after a 20% discount an item costs 480. What was the original price?

  • The factor for a 20% decrease is 0.8
  • Original = 480 ÷ 0.8 = 600

Check: 20% of 600 is 120, and 600 − 120 = 480. Correct. A common slip is to add 20% to 480, which gives 576 and is wrong, because the 20% applied to the original, not the discounted price.

Chained changes do not add up

When two percentage changes follow each other, multiply the factors. Do not add the percentages.

Example: a value of 100 rises by 20%, then falls by 20%.

  • After the rise: 100 × 1.2 = 120
  • After the fall: 120 × 0.8 = 96

The result is 96, a net fall of 4%, not zero. The second percentage applied to a bigger base.

Putting it together: a small shopping example

A jacket is marked at 3,200. The shop offers 25% off, and a coupon then takes a further 10% off the reduced price.

  • After 25% off: 3,200 × 0.75 = 2,400
  • After the coupon: 2,400 × 0.9 = 2,160
  • Overall saving: 3,200 − 2,160 = 1,040, and 1,040 ÷ 3,200 = 0.325, so 32.5%

The combined discount is 32.5%, not 35%, because the coupon applied to the already reduced price. Multiplying the factors, 0.75 × 0.9 = 0.675, gives the same answer: you pay 67.5% of the original, so you save 32.5%.

Common mistakes

  • Using the wrong base. For changes, the base is the starting value. For "what percent of", the base is the whole.
  • Confusing percent and percentage points. If a rate moves from 8% to 10%, it rose by 2 percentage points, but by 25% in relative terms (2 ÷ 8 = 0.25).
  • Subtracting a percentage from an inclusive total. Reverse calculations need division by the factor, as in case 7. The same trap catches people removing a tax from a total.
  • Adding chained percentages. Multiply the factors instead.
  • Rounding too early. Round at the final step, especially when chaining.

Quick checklist

  1. Write down the whole, the part, or the old and new values.
  2. Decide which of the seven cases it is.
  3. Choose the right base.
  4. Calculate, then check by going the other way.

The percentage calculator covers these cases without manual work. For tax-style percentages, the GST calculator applies case 1 and case 7 to prices. If you are converting exam scores, the CGPA calculator uses related ratio arithmetic.

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