How to Calculate Percentage Increase and Decrease

Use the original value as the reference

The general formula is:

Percentage change = (new value − original value) ÷ original value × 100

First calculate the numerical difference. Then divide that change by the original value—the value you started from. Multiplying by 100 expresses the result as a percentage.

A positive result is an increase and a negative result is a decrease. You can report −20% as “a 20% decrease” when that wording is clearer.

Worked percentage increase example

A monthly price rises from £80 to £100:

1. Change: £100 − £80 = £20.
2. Compare with the original: £20 ÷ £80 = 0.25.
3. Convert to a percentage: 0.25 × 100 = 25%.

The increase is 25%. A common error is dividing by the new £100 value, which would give 20%. Percentage change normally asks how large the change is relative to where the value began.

An increase can exceed 100%. A rise from 40 to 100 is a change of 60; 60 ÷ 40 × 100 = 150%.

Worked percentage decrease example

A price falls from £100 to £80:

1. Change: £80 − £100 = −£20.
2. Compare with the original: −£20 ÷ £100 = −0.20.
3. Convert to a percentage: −0.20 × 100 = −20%.

This is a 20% decrease. Notice that £80 to £100 was a 25% increase, while £100 to £80 is a 20% decrease. The £20 difference is identical, but each comparison uses a different original value.

Apply an increase or decrease with a multiplier

To increase a value by a known percentage, add the percentage to 100% and multiply. A 15% increase leaves a multiplier of 1.15:

New value = original value × 1.15

To decrease by 15%, 85% remains, so multiply by 0.85. For £240, a 15% increase gives £276, while a 15% decrease gives £204.

This method calculates the new amount from a known change rate. The earlier formula calculates the rate when the old and new amounts are known.

Reverse a percentage change correctly

Equal increases and decreases do not cancel because the base changes. £100 increased by 20% becomes £120. Reducing £120 by 20% removes £24 and leaves £96.

To reverse a 20% increase, divide the new value by 1.20. To reverse a 20% decrease, divide by 0.80. If a sale price is £72 after 20% off, the original was £72 ÷ 0.80 = £90.

When several changes occur, apply each multiplier in sequence. A 10% rise followed by 5% growth uses 1.10 × 1.05 = 1.155, a combined increase of 15.5%, not 15%.

Percentage change versus percentage points

If an interest rate moves from 20% to 25%, it has risen by 5 percentage points. Relative to the starting 20%, the increase is 5 ÷ 20 × 100 = 25%.

Both statements can be correct, but they answer different questions. Use percentage points for the arithmetic gap between rates and percentage change for the size of the movement relative to the old rate.

Compare like-for-like time periods

A correct formula can still produce a misleading comparison when the periods differ. Compare a full month with another full month, or adjust for the number of days when that is appropriate. Seasonal businesses should avoid treating December-to-January movement as a normal monthly trend without context.

Example: website visits rise from 8,000 in a 28-day month to 9,000 in a 31-day month. The headline increase is 12.5%, but average daily visits move only from about 286 to about 290—roughly a 1.6% increase. The daily rates provide a separate, often useful comparison.

When presenting change, include the original value, new value, period and formula. “Up 25%” is less informative than “monthly orders increased from 400 in June to 500 in July, a 25% rise.” For very small starting numbers, show the absolute change too because a dramatic percentage may represent only a few units.

Handle zero and negative values carefully

Standard percentage change is undefined when the original value is zero because division by zero is impossible. It is better to report the absolute change or explain that the value rose from zero.

Negative starting values can produce mathematically valid but unintuitive results, especially for losses, temperatures or debt. State the raw values and context rather than presenting a percentage alone.

Also distinguish a measured change from cause. A 30% rise in one period describes the numbers; it does not explain why they moved or guarantee the trend will continue.

Common mistakes to avoid

• Dividing by the new value instead of the original.
• Confusing an absolute difference with a percentage difference.
• Assuming equal rises and falls cancel.
• Adding successive rates instead of compounding them.
• Calling percentage points “per cent” without clarification.
• Using the standard formula when the starting value is zero.

For shopping reductions, see percentage discounts. For finding a percentage of an amount, see the general percentage guide.

Percentage change worked examples

40 to 55: the increase is 15. Divide 15 by the original 40 and multiply by 100 to get a 37.5% increase. 80 to 60: the decrease is 20. Divide 20 by the original 80 and multiply by 100 to get a 25% decrease.

Always divide by the original value, not the new value. Use the UsefulFox Percentage Calculator for a quick percentage calculation.

Frequently asked questions