Percentage Change Calculator

Calculate the percentage increase or decrease from an old value to a new value. The initial value is the baseline: positive results indicate an increase and negative results indicate a decrease.

Enter two values

For a standard calculation, enter the initial and final values. To reverse solve, leave the value you want to find blank.

The baseline (old value). It cannot be zero when calculating a percentage.
The new value after the increase or decrease.

Result

Enter the initial and final values to see the result.
Initial value
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Final value
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Numeric change
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Percentage change
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Direction
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Multiplier
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Final as % of initial
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The direction and meaning of the result will appear here.
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Enter two values to see the calculation steps.
Reverse solve for an initial or final value
Use a positive number for an increase and a negative number for a decrease. Enter this plus either value, leaving the unknown value blank.
The signed formula has two branches, so the baseline sign is required.
Decimals and repeated calculations

Results update instantly when exactly two valid fields are entered. Ctrl/Cmd + Enter calculates; Esc clears.

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Percentage change explained

Percentage change measures how far a final value moved relative to the magnitude of its initial value. This page uses the signed result: a positive percentage is an increase, a negative percentage is a decrease, and zero means no change.

Percentage change formula

Initial is the old or baseline value. Final is the new value. Vertical bars in |Initial| mean absolute value, or distance from zero.

Percentage increase
(Final − Initial) ÷ |Initial| × 100%, used when Final > Initial.
Percentage decrease
(Initial − Final) ÷ |Initial| × 100%, reported as a positive decrease amount when Final < Initial.

How to calculate percentage change

  1. Subtract the initial value from the final value.
  2. Divide that numeric change by the magnitude of the initial value.
  3. Multiply by 100 to express the result as a percentage.
  4. Interpret a positive sign as an increase and a negative sign as a decrease.

For example, a price rising from £40 to £46 changes by £6; £6 ÷ £40 × 100 = 15%. The price increased by 15%. The same method can describe salary from £30,000 to £31,500 (5% increase), revenue from 200,000 to 180,000 (10% decrease), population from 8,000 to 8,400 (5% increase), a test score from 72 to 81 (12.5% increase), or a measurement from 2.4 cm to 2.1 cm (12.5% decrease).

Percentage increase versus percentage decrease

The signed general formula handles both. If the final value is larger, the numerator is positive and the answer is an increase. If the final value is smaller, the numerator is negative and the answer is a decrease. When writing a decrease without a sign, use its magnitude: −20% means a 20% decrease.

Changes are directional, not reversible. A fall from 100 to 50 is a 50% decrease, but recovering from 50 to 100 requires a 100% increase because the second calculation uses the smaller value, 50, as its baseline.

Percentage change versus percentage difference

Percentage change is directional and uses the initial value as the denominator. Use it when one value clearly comes before the other. Percentage difference treats two values symmetrically and usually divides their absolute difference by their average. Use percentage difference when neither value is the baseline, such as comparing two independent measurements.

Percentage change versus percentage-point change

Percentage points compare two percentages by subtraction. If a test pass rate rises from 40% to 50%, it rises by 10 percentage points, but the relative percentage increase is (50 − 40) ÷ 40 × 100 = 25%. These statements describe different quantities.

Why the initial value is the denominator

The question is “how large was the movement compared with where it started?” The initial value supplies that reference. A change of 10 is large relative to an initial value of 20 (50%) but small relative to an initial value of 1,000 (1%). Swapping the values changes the reference and therefore changes the answer.

Worked examples

Percentage increase: 120 to 150

  1. Substitute: (150 − 120) ÷ |120| × 100.
  2. Subtract: 150 − 120 = +30.
  3. Divide by the baseline magnitude: 30 ÷ 120 = 0.25.
  4. Multiply by 100: 0.25 × 100 = +25%.

Interpretation: 150 is 25% higher than 120.

Percentage decrease: 80 to 50

  1. Substitute: (50 − 80) ÷ |80| × 100.
  2. Subtract: 50 − 80 = −30.
  3. Divide: −30 ÷ 80 = −0.375.
  4. Multiply: −0.375 × 100 = −37.5%.

Interpretation: 50 is 37.5% lower than 80.

Negative to negative: −40 to −20

  1. Substitute: (−20 − (−40)) ÷ |−40| × 100.
  2. Subtract: −20 + 40 = +20.
  3. Divide: 20 ÷ 40 = 0.5.
  4. Multiply: 0.5 × 100 = +50%.

Interpretation: the number increased by 20, moving closer to zero; under the absolute-baseline convention this is a 50% increase.

Crossing negative to positive: −20 to 10

  1. Substitute: (10 − (−20)) ÷ |−20| × 100.
  2. Subtract: 10 + 20 = +30.
  3. Divide: 30 ÷ 20 = 1.5.
  4. Multiply: 1.5 × 100 = +150%.

Interpretation: the value increased by 30 and crossed zero, a 150% increase relative to the starting magnitude.

No change: 75 to 75

  1. Substitute: (75 − 75) ÷ |75| × 100.
  2. Subtract: 75 − 75 = 0.
  3. Divide: 0 ÷ 75 = 0.
  4. Multiply: 0 × 100 = 0%.

Interpretation: the values are equal, so there is no change.

Zero initial value: 0 to 10

  1. Substitute: (10 − 0) ÷ |0| × 100.
  2. Subtract: 10 − 0 = +10.
  3. The next step would require 10 ÷ 0.
  4. Division by zero is undefined, so no percentage can be calculated.

Interpretation: the numeric change is +10, but the percentage change is undefined. It should not be labeled infinite.

Edge cases and interpretation

  • Initial value of zero: percentage change is undefined because the formula requires division by zero. Report the numeric difference instead.
  • Negative initial values: this calculator divides by |Initial|, so the result sign follows the numeric direction. Moving from −40 to −20 is positive; moving from −20 to −40 is negative. Some fields use different conventions, so state the convention when reporting.
  • Changes beyond 100%: these can be valid. From 50 to −10 is −120% because the value fell by more than the entire starting magnitude.
  • Rounding: calculate with unrounded numbers and round only the displayed answer.

Editorial review: Formula, reverse-solving branches, examples, zero-baseline handling, and accessibility behavior were checked by the Starlight Tools Editorial Team using independent substitution and boundary tests. Last reviewed: July 14, 2026. Last updated: July 14, 2026. Calculations run locally in your browser; entered values are not uploaded.

Frequently asked questions

What is the formula for percentage change?

Percentage change = ((final value − initial value) ÷ |initial value|) × 100. A positive result is an increase and a negative result is a decrease.

What happens when the initial value is zero?

Percentage change is undefined because the formula would divide by zero. You can still report the numeric change.

How does percentage change work with negative values?

This calculator divides by the magnitude of the initial value, |initial|. The result's sign therefore follows the numeric direction from initial to final.

Why does swapping the initial and final values change the percentage?

The initial value is the denominator, so swapping values changes the baseline. A 50% decrease from 20 to 10 becomes a 100% increase from 10 to 20.

Can a percentage decrease be more than 100%?

Yes, when the final value passes below zero. From 50 to −10, the change is −60 and the percentage change is −120%.

How do I calculate percentage change in Excel or Google Sheets?

If the initial value is in A2 and the final value is in B2, use =(B2-A2)/ABS(A2), then format the cell as a percentage.

How do I find the original value from a percentage change?

For a positive initial value, divide the final value by 1 + p/100, where p is the signed percentage change. For example, 150 after a 25% increase started at 150 ÷ 1.25 = 120. For a negative initial value under this page's convention, divide by 1 − p/100; the calculator's sign option handles this branch.

What is the percentage change from 20 to 10?

((10 − 20) ÷ 20) × 100 = −50%, so it is a 50% decrease.

What is the percentage change from 50 to 75?

((75 − 50) ÷ 50) × 100 = +50%, so it is a 50% increase.

Are my inputs private?

Yes. Calculations run locally in your browser and the calculator does not upload your entered values.

5 Fun Facts about Percentage Change

A 50% drop needs 100% back

Fall from 100 to 50? You must double (100%) to return—percentage change is always relative to the starting point.

Base effect

Zero has no percentage baseline

Any non-zero move from 0 has an undefined percentage change because the formula would require division by zero.

Math quirk

Compounding hides in plain sight

A steady 1% daily increase is +37.8x over a year (≈3,678%). Small changes stack explosively.

Everyday exponential

Negative starts still work

Using |Old| in the formula lets you compare changes from negative baselines—handy for net losses flipping to gains.

Handles negatives

Rounding can flip the story

A 0.49% dip rounds to 0% at one decimal, but a 0.51% rise rounds to +0.5%. Precision settings shape the headline.

Data storytelling

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