3 Basic Percentage Calculations — Formulas and Everyday Examples
B% of A, A is what percent of B, and percent change. Most percentage problems come down to these three formulas, explained with tips, test scores and pay raises.
A percent (%) is 'a share out of 100'. 25% means 25 out of 100, or 0.25. Percentage problems may look different, but almost all of them are one of the three types below. Once you recognise the type, the formula is simple.
1. What is B% of A?
The most common type. Multiply the whole (A) by the rate (B%).
B% of A = A × B ÷ 100
- 15% tip on a $48.00 dinner bill → 48 × 15 ÷ 100 = $7.20
- Saving 20% of a $3,200,000 annual payroll budget → 3,200,000 × 0.2 = $640,000
- 92% attendance out of 350 members → 350 × 0.92 = 322 people
Converting the percentage to a decimal speeds things up. 15% is 0.15, 8% is 0.08 and 120% is 1.2. Just drop the percent sign and move the decimal point two places to the left.
2. A is what percent of B?
This finds the share a part takes up of the whole. Divide the part by the whole, then multiply by 100.
A is (A ÷ B × 100)% of B
- 68 correct answers out of 80 questions → 68 ÷ 80 × 100 = 85%
- $120 thousand of ad spend in a $500 thousand budget → 120 ÷ 500 × 100 = 24%
The thing to watch is which value is the base (denominator). 'Ad spend is what percent of the budget?' and 'The budget is what percent of ad spend?' are completely different questions. The value after 'of' is the base (denominator).
3. By what percent did A increase (decrease) to B?
This expresses the size of a change as a ratio of the starting value.
Percent change = (B − A) ÷ A × 100
- Salary $40,000 → $43,000: (43,000 − 40,000) ÷ 40,000 × 100 = 7.5% raise
- Monthly visitors 12,000 → 9,000: (9,000 − 12,000) ÷ 12,000 × 100 = −25% (a 25% decrease)
A positive result is an increase and a negative one is a decrease. The base is always the value before the change. Using 9,000 as the base gives 33.3%, which answers a different question: 'the rate of increase from 9,000 to 12,000'.
Telling the three types apart
- You know the rate (%) and want an amount → type 1 (multiply)
- You know two amounts and want a rate → type 2 (divide)
- You know the before and after values of the same thing and want the rate of change → type 3 (divide the difference by the starting value)
Mental math tips
- For 10%, move the decimal point one place left: 10% of 37,500 = 3,750
- 5% is half of 10%, 20% is double 10%, and 15% is 10% + 5%
- For 1%, move it two places: 1% of 37,500 = 375 → 3% is 1,125
- B% of A = A% of B: 8% of 50 equals 50% of 8, which is 4. If one side is easier, swap them.
Common mistakes
- Multiplying by the raw percentage: 200 × 15 = 3,000 is wrong; 200 × 0.15 = 30
- Putting the changed value in the denominator of a percent change
- Adding a % sign to the difference between two percentages: going from 3% to 5% is not a '2% increase' but a 2 percentage point (2%p) increase (a 66.7% increase in relative terms). See the percentage point guide for details.