How to Calculate Percentage Increase and Decrease (With Examples)

One Formula, Two Directions

Pay rises, sale prices, energy bills, website traffic, exam results — almost every number worth tracking gets compared to what it used to be. That comparison is a percentage change, and whether the number went up or down, you only ever need one formula:

Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100

A positive answer is an increase. A negative answer is a decrease. There is no separate formula for the two directions — the minus sign does that work for you.

The single most important detail is hiding in the denominator: you always divide by the original value, never the new one. Almost every percentage error traces back to that one step.

Calculating a Percentage Increase

Example: Your salary rises from £28,000 to £29,540. What is the percentage increase?

Find the difference: 29,540 − 28,000 = 1,540
Divide by the original: 1,540 ÷ 28,000 = 0.055
Multiply by 100: 0.055 × 100 = a 5.5% increase

Calculating a Percentage Decrease

Example: A jacket is reduced from £240 to £180. What is the percentage decrease?

Find the difference: 180 − 240 = −60
Divide by the original: −60 ÷ 240 = −0.25
Multiply by 100: −0.25 × 100 = a 25% decrease

The negative sign simply tells you the direction. In writing, you drop it and say “a 25% decrease” rather than “a −25% increase”.

The Denominator Trap

Dividing by the new value instead of the original quietly changes the answer, and the mistake is invisible unless you check.

Correct: 60 ÷ 240 = 25% decrease.
Wrong: 60 ÷ 180 = 33.3%.

Both look plausible on a page. Only the first one is the percentage decrease — the second is answering a different question entirely (by how much would you have to increase £180 to get back to £240).

Why +50% Then −50% Does Not Bring You Home

This is the percentage fact that surprises people most, and it has real consequences for investments and discounts.

Start with £100. Add 50% and you have £150. Now take 50% off that, and you land on £75 — not £100. You are 25% down despite the two percentages looking like they cancel.

The reason is the denominator again: the 50% rise was calculated on £100, but the 50% fall was calculated on the larger £150. Equal percentages applied to unequal bases give unequal amounts.

How Much Does It Take to Recover?

To undo an increase, the decrease you need is always smaller than the rise:

Undo a +25% rise → you need a 20% fall
Undo a +50% rise → you need a 33.3% fall
Undo a +100% rise → you need a 50% fall

Run in reverse, this is why a portfolio that drops 50% needs a 100% gain just to break even.

Working Backwards From the New Price

Sometimes you know the result and need the starting point — a sale price, say, when you want to check the discount was real. You cannot get there by adding the percentage back on. You divide:

Original = New Value ÷ (1 + change as a decimal)

Example: A coat costs £48 in a 20% off sale. 48 ÷ 0.80 = £60 before the discount.

Adding 20% back to £48 gives £57.60, which is wrong, because that 20% would be calculated on the discounted price rather than the original. This is exactly the arithmetic that catches people out when they try to strip VAT from a receipt by subtracting 20%.

Percentage Points Are Not Percent

If an interest rate moves from 2% to 3%, has it risen by 1% or by 50%? Both, depending on what you are measuring — which is why the two have different names.

It rose by 1 percentage point (3 − 2), the absolute gap.
It rose by 50% (1 ÷ 2), the relative change.

Mixing these up makes a modest change sound dramatic, or a dramatic one sound modest. When the underlying figure is already a percentage — interest rates, unemployment, market share, conversion rates — say “percentage points” when you mean the gap, and “percent” when you mean the change relative to where it started.

The Other Two Percentage Questions

Percentage change is one of three everyday calculations. The other two are simpler but worth stating plainly:

Finding a Percentage of a Number

Result = (Percentage ÷ 100) × Number

18% of 250 = 0.18 × 250 = 45

Finding What Percentage One Number Is of Another

Result = (Part ÷ Whole) × 100

35 out of 140 = 35 ÷ 140 = 0.25 = 25%

Quick Reference: Percentage Multipliers

For repeated calculations, skip the two-step method and multiply once:

Add 5%: × 1.05
Add 20%: × 1.20
Add 100%: × 2.00
Take off 10%: × 0.90
Take off 25%: × 0.75
Take off 40%: × 0.60

To reverse any of them, divide by the same multiplier instead.

Conclusion

Percentage change comes down to three habits: subtract, divide by the original, and multiply by 100. Remember that percentages do not cancel out, that working backwards means dividing rather than adding, and that a percentage point is a different animal from a percent. Get those right and you can check a pay rise, audit a discount, or read a statistic without being misled. When the numbers get awkward, run them through a Percentage Calculator so the direction and the denominator are handled for you.

Try our Percentage Calculator

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