Percentage Change – One Formula for Everything

Percentage change is a single formula that covers both increases and decreases. It tells you how large a change is relative to the starting value, making it the standard way to compare changes across different situations.

The Formula

Percentage Change = ((New Value minus Original Value) / Original Value) times 100. A positive result is an increase; a negative result is a decrease.

Worked Examples

A stock rises from 200 to 250.

Change = 250 - 200 = 50. (50 / 200) times 100 = +25% (increase).

Temperature drops from 20 degrees to 15 degrees.

Change = 15 - 20 = -5. (-5 / 20) times 100 = -25% (decrease).

A salary changes from 24,000 to 26,400.

(26400 - 24000) / 24000 times 100 = 2400/24000 times 100 = +10%.

Test score drops from 80 to 64.

(64 - 80) / 80 times 100 = -16/80 times 100 = -20%.

Finding a New Value from a Percentage Change

Change	Multiplier	Example
+15%	1.15	300 times 1.15 = 345
-20%	0.80	500 times 0.80 = 400
+100%	2.00	Value doubles
-50%	0.50	Value halves

Successive Percentage Changes

When multiple percentage changes happen one after another, multiply the multipliers together.

A price increases by 20% and then falls by 10%.

Combined multiplier = 1.20 times 0.90 = 1.08. Net effect: +8% increase. (Not 10% — order and multiplication matter.)

A population grows 5% per year for 3 years.

Combined multiplier = 1.05 times 1.05 times 1.05 = 1.1576. Net effect: +15.76%.

Common Mistakes

Dividing by the new value instead of the original — always use the original as the denominator.
Adding successive percentages: a 20% rise followed by a 20% fall does NOT return to the original value.
Confusing the result of a percentage change with the percentage itself.

Key Takeaways

Percentage change = (change / original) times 100. Positive means increase; negative means decrease.
Always divide by the original (starting) value.
For successive changes, multiply the multipliers, not the percentages.
A 50% increase followed by a 50% decrease does not return to the start: 100 times 1.5 times 0.5 = 75.

Practice Questions

A house value rises from 180,000 to 207,000. Find the percentage change.
A company employed 450 people last year and 360 this year. Find the percentage change.
A value increases by 30% and then decreases by 30%. What is the net percentage change?
A price increases by 10% each year for 2 years. What is the total percentage increase?
A smartphone was 800. After one year it is 600 and after two years it is 480. Find the percentage change in each year and the total change.