Pythagorist
Percentages

Percentage Change Calculator

Calculate the percentage change between two values. Enter the original and new values to find the percentage increase or decrease, with full step-by-step working using the standard formula.

Increase

+25%

How it works

  1. Find the difference

    100−80=20100 - 80 = 20

    Subtract the original value from the new value: 100 − 80 = 20.

    Result:20

  2. Divide by the original value

    2080=0.25\frac{20}{80} = 0.25

    Divide the difference by the original value: 20 ÷ 80 = 0.25.

    Result:0.25

  3. Multiply by 100

    0.25×100=25%0.25 \times 100 = 25\%

    Multiply by 100 to get the percentage: 25%. This is a percentage increase.

    Result:25% increase

The formula

% change=new value−original valueoriginal value×100\text{\% change} = \frac{\text{new value} - \text{original value}}{\text{original value}} \times 100
NewvalueNew valueThe value after the change
OriginalvalueOriginal valueThe starting value

Example substitution

120−100100×100=20%\frac{120 - 100}{100} \times 100 = 20\%

From 100 to 120: difference is 20, divide by original (100), multiply by 100 = 20% increase.

Worked examples

A jacket costs £40 then rises to £50. What is the % increase?

  1. 1
    Difference: 50 − 40 = 10
  2. 2
    Divide by original: 10 ÷ 40 = 0.25
  3. 3
    Multiply by 100: 25%
Answer: 25% increase

A score drops from 80 to 60. What is the % decrease?

  1. 1
    Difference: 60 − 80 = −20
  2. 2
    Divide by original: −20 ÷ 80 = −0.25
  3. 3
    Multiply by 100: 25%
Answer: 25% decrease

A population grows from 5000 to 6500. What is the % increase?

  1. 1
    Difference: 6500 − 5000 = 1500
  2. 2
    Divide by original: 1500 ÷ 5000 = 0.3
  3. 3
    Multiply by 100: 30%
Answer: 30% increase

Frequently asked questions

What is the formula for percentage change?+

Percentage change = ((new − original) / original) × 100. Positive = increase, negative = decrease.

How do you calculate a 15% increase?+

Multiply the original value by 1.15. E.g., 15% increase on £200 = 200 × 1.15 = £230.

What is percentage change from 50 to 75?+

((75 − 50) / 50) × 100 = (25/50) × 100 = 50% increase.

How do you find a percentage decrease?+

Use the same formula as increase. A negative result indicates a decrease. E.g., 100 to 80: ((80−100)/100) × 100 = −20%, so a 20% decrease.

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