mathsolvers.io
Percentages

Percentage Increase / Decrease Calculator

Calculate the percentage change between any two values — with the full formula and every step shown. Covers price changes, salary increases, population growth, exam score differences, and more.

Percentage change calculator

↓
Related Calculators
Percentage of a Number → Reverse Percentage → All 3 Types Together →

Step by step calculations

Enter values in the calculator to see the step by step calculations.

Percentage Increase / Decrease Calculator Explained

Core concepts, classroom applications, and plain-English explanations for all audiences.

Where percentage change hits you daily

Your rent goes up from £950 to £1,050 — that's a 10.5% increase. Inflation runs at 4% and your pay rise is 3% — you're actually worse off. A house bought for £220,000 sells for £285,000 — that's a 29.5% gain. Every financial headline uses percentage change; knowing how to check it yourself is a genuine power move.

Worked example

"A jacket costs £85 in a sale, down from £120. What is the percentage decrease?"

Change = 85 − 120 = −35

% change = (−35 ÷ 120) × 100

= −0.2917 × 100

Result: −29.2% (a decrease of 29.2%)

Always divide by the ORIGINAL value (120), not the new one.

The critical distinction

  • → Percentage change vs percentage points: If interest rates go from 3% to 5%, that's a 2 percentage point increase — but a 66.7% change. These are completely different things. News reports mix them up constantly.
  • ✗ +25% then −25% ≠ back to start: Up 25% then down 25% leaves you at 93.75% of your original — a net loss of 6.25%.

Formula to remember

% change = (New − Original) ÷ Original × 100. Positive = increase. Negative = decrease. Always original in the denominator.

Good to know

Understanding percentage change

Δ
The formula
Percentage change = (New − Original) ÷ Original × 100. A positive result is an increase; negative is a decrease. The key is always dividing by the original value, not the new one — a common mistake is to divide by the new value, which gives the wrong answer.
From 80 to 100:
(100 − 80) ÷ 80 × 100
= 20 ÷ 80 × 100
= 0.25 × 100 = 25%
!
Increases and decreases are not symmetrical
If a price increases by 25% then decreases by 25%, you do not end up back where you started. A 25% increase from 80 gives 100. But a 25% decrease from 100 gives 75 — not 80. This is because the base value changes. This asymmetry matters hugely in finance, investing and statistics.
+25% then −25%:
80 × 1.25 = 100
100 × 0.75 = 75 (not 80!)

Net change from 80 to 75:
(75 − 80) ÷ 80 × 100 = −6.25%