Calquly
Math

Percentage Increase and Decrease Calculator

Enter where you started and where you ended up. The calculator names the direction, the size of the move and the multiplier behind it.

This calculator needs JavaScript to run. The formula, the worked examples and the explanations below all work without it.

Live result — no button needed.

How percentage change works

Percentage change always measures the move relative to where you started. That starting value is the denominator, and it is the reason the same pair of numbers gives two different answers depending on which direction you travel.

Formulapercentage change = (new − old) ÷ |old| × 100

Going from 80 to 100 is a 25% increase, because the 20-point gain is measured against 80. Going back from 100 to 80 is a 20% decrease, because the same 20-point gap is now measured against 100. Neither is wrong — they answer different questions.

How to calculate it by hand

  1. Subtract the old value from the new one. Keep the sign: a negative result means a decrease.
  2. Divide that difference by the old value.
  3. Multiply by 100 to turn the decimal into a percentage.

Example: rent goes from $1,450 to $1,595. The difference is $145. Divide by 1,450 to get 0.1, multiply by 100 — a 10% increase.

The shortcut worth memorising is the multiplier. A 10% increase is × 1.10, a 25% decrease is × 0.75. Multipliers chain cleanly, which is why they are how spreadsheets and finance people actually do this.

Worked examples

A stock moves from $42.50 to $39.10. What happened?

(39.10 − 42.50) ÷ 42.50 × 100 = −8%. An 8% decrease.

Traffic grew from 1,200 to 4,800 visits.

(4800 − 1200) ÷ 1200 × 100 = +300%. The new figure is four times the old one, which is a 300% increase — not 400%.

After a 25% raise a salary is $75,000. What was it before?

Use Find the original value: 75,000 ÷ 1.25 = $60,000. Dividing by the multiplier is the only correct way back — taking 25% off $75,000 would give $56,250, which is wrong.

The mistakes worth knowing about

Percentage points are not percentages. If a rate goes from 4% to 6%, that is a rise of 2 percentage points but a 50% increase. News stories mix these up constantly, and the difference is often the whole story.

An increase and a decrease of the same size do not cancel out. Lose 50% and you need a 100% gain to get back to where you were. This calculator will show you why: the denominator changed.

You cannot start from zero. Any increase from 0 is infinite in percentage terms, so the calculator tells you rather than printing a meaningless number. Report the absolute change instead.

Negative starting values are handled by dividing by the absolute value of the original, so a move from −50 to −25 reads as a 50% increase. That matches how financial reporting treats losses shrinking.

Common uses

  • Salary and rent: checking that a raise or an increase matches what was announced.
  • Business reporting: month-on-month and year-on-year growth.
  • Prices: how much something has gone up since you last bought it.
  • Science and lab work: percent change between two measurements.
  • Fitness and weight: change relative to a starting figure.

Frequently asked questions

What is the formula for percentage increase?
(new value − old value) ÷ old value × 100. If the result is positive it is an increase, if it is negative it is a decrease. Dividing by the old value is the part people get wrong.
Why is a 50% decrease followed by a 50% increase not back to the start?
Because the second percentage is taken from a smaller number. $100 minus 50% is $50; adding 50% of $50 gives $75, not $100. To recover from a 50% loss you need a 100% gain.
What is the difference between percentage change and percentage difference?
Percentage change has a direction and a defined starting point. Percentage difference compares two values against their average and gives the same answer whichever order you enter them. If neither number is "the original", you want the percentage difference tab on the percentage calculator.
Can I calculate a percentage change from zero?
No, and no calculator can honestly. Dividing by zero is undefined, so a move from 0 to any number has no meaningful percentage. State the absolute change instead — "up by 40 units" rather than "up by ∞%".
How do I reverse a percentage increase?
Divide by the multiplier rather than subtracting the percentage. To undo a 20% increase, divide by 1.20. The "Find the original value" tab does exactly this.
What is a percentage point?
A plain difference between two percentages. Going from 4% to 6% is 2 percentage points, and also a 50% increase. Use percentage points when both numbers are already percentages, to avoid ambiguity.