Percentage Increase & Decrease Calculator
Find the percentage increase or decrease between two numbers, add or take off a percentage, or work back to the original value, with every step shown. Advanced adds points, changes in a row, average % per period and % difference.
For rates such as interest rates, tax rates, unemployment or poll shares.
Switching unit keeps the same length of time (5 years becomes 60 months). For investments with dates, inflation and tax, use the CAGR calculator.
For two values with no "before" and "after", such as two shops' prices or two measurements.
Auto shows percentages to 2 places and other numbers to up to 4 (money to 2).
Step-by-step table
How your percentage change is worked out
Change ÷ old value × 100. A rise is +, a fall is −.
- 1
Find the change
100 − 80= +20
- 2
Divide by the old value
+20 ÷ 80= 0.25
- 3
Times 100
0.25 × 100= +25% (increase)
- 4
To undo it
100 back to 80−20 ÷ 100= −20%
Read more: the formulas, worked examples and common traps
A percentage change compares how much something moved with where it started. A rise gives a positive answer (a percentage increase) and a fall gives a negative one (a percentage decrease). The key rule behind every tool on this page: a percentage is always worked out on a starting value, so you multiply by 1 + the change, and you divide by it to go backwards. For "X% of a number" and other everyday sums, use the percentage calculator.
The formula
% change = (new − old) ÷ old × 100
new value = old × (1 + % ÷ 100) for an increase, old × (1 − % ÷ 100) for a decrease
original = final ÷ (1 + % ÷ 100) after an increase, final ÷ (1 − % ÷ 100) after a decrease
percentage points = new % − old %
changes in a row = (1 + first ÷ 100) × (1 + second ÷ 100) × … − 1, then × 100
average % per period = ((end ÷ start)^(1 ÷ periods) − 1) × 100
% difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Worked example
A price goes from 80 to 100. The change is 100 − 80 = 20. Divide by the old value: 20 ÷ 80 = 0.25. Times 100: +25%, a 25% increase. Going back from 100 to 80 is a change of −20, and −20 ÷ 100 × 100 = −20%, so a 25% rise is undone by a 20% fall, not a 25% one.
Increase 200 by 15%: 200 × 1.15 = 230 (15% of 200 is 30). Work it back: 230 ÷ 1.15 = 200. Taking 15% off 230 gives 230 × 0.85 = 195.5, which is wrong.
Average per period: 1,000 grows to 1,500 in 5 years. 1,500 ÷ 1,000 = 1.5, and 1.5^(1/5) = 1.0845, so the average is 8.45% a year. Check it: 1,000 × 1.08455 ≈ 1,500. The total change is 50%, but 50 ÷ 5 = 10% a year is too high, because each year's growth builds on the last.
| Question | Sum | Default example |
|---|---|---|
| % change from old to new | (new − old) ÷ old × 100 | 80 → 100 is +25% |
| Increase or decrease by % | value × (1 ± % ÷ 100) | 200 + 15% = 230 |
| Original before a change | final ÷ (1 ± % ÷ 100) | 230 after +15% was 200 |
| Percent vs points | new % − old % | 3% → 5% is +2 points, +66.67% |
| Changes in a row | multiply the (1 + %) parts | +10% then −10% is −1% |
| Average % per period | (end ÷ start)^(1 ÷ n) − 1 | 1,000 → 1,500 in 5 years is 8.45% a year |
| % difference | |A − B| ÷ mean × 100 | 10 and 20 differ by 66.67% |
Rises and falls don't cancel out
100 up 10% is 110, and 10% off 110 is 11, so it ends at 99: 1% down overall. The same happens the other way round. Changes in a row multiply: 1.10 × 0.90 = 0.99. To undo a rise of P%, you need a fall of P ÷ (100 + P) × 100; to undo a 25% rise that is 25 ÷ 125 × 100 = 20%.
| Rise | Fall that undoes it | Fall | Rise that undoes it |
|---|---|---|---|
| +10% | −9.09% | −10% | +11.11% |
| +20% | −16.67% | −20% | +25% |
| +25% | −20% | −25% | +33.33% |
| +50% | −33.33% | −50% | +100% |
| +100% | −50% | −75% | +300% |
Prices before tax or a discount
Sales tax, VAT or GST is added as a percentage of the price before tax, so to remove it you divide by 1 + the rate: a price of 230 including 15% tax is 230 ÷ 1.15 = 200 before tax, and the tax is 30. A sale price of 170 after 15% off was 170 ÷ 0.85 = 200. Tax rates differ by country and product, so enter the rate that applies to you.
Percentage points or percent?
If an interest rate moves from 3% to 5%, it is up 2 percentage points, which is a 66.67% rise in the rate itself. Both are true, but they mean different things, so news about interest rates, tax rates and polls should use points.
Percentage difference or percentage change?
Percentage change has a before and an after and divides by the old value, so 10 → 20 is +100% but 20 → 10 is −50%. Percentage difference compares two values with no order, such as two shops' prices, and divides by their average, so 10 and 20 differ by 10 ÷ 15 × 100 = 66.67% whichever way round.
Negative numbers and zero
A change from 0 cannot be a percentage (it would be infinite), so the old value must not be 0. When the old value is negative, this calculator divides by its size, so a move from −50 to −25 counts as a +50% rise, the usual convention for things like profit and loss. The average per period needs the start and end to have the same sign.
Common questions
How do I calculate a percentage increase?
Take the old value away from the new one, divide by the old value and multiply by 100. A price that rises from 80 to 100 has gone up by (100 − 80) ÷ 80 × 100 = 25%. If the answer is negative, the value has fallen, so it is a percentage decrease.
How do I increase or decrease a number by a percentage?
Multiply by 1 plus the percentage as a decimal to increase it, or by 1 minus it to decrease it. 200 increased by 15% is 200 × 1.15 = 230, and 200 decreased by 15% is 200 × 0.85 = 170.
How do I find the original price before a percentage was added?
Divide the final price by 1 plus the percentage as a decimal. A price of 230 that includes a 15% increase was 230 ÷ 1.15 = 200. Taking 15% off 230 gives 195.5, which is wrong, because the 15% was worked out on 200. After a discount, divide by 1 minus the percentage instead.
Why doesn't a 10% rise followed by a 10% fall get back to where I started?
Because the fall is worked out on a bigger number. 100 rises 10% to 110, and 10% of 110 is 11, so it falls to 99: a 1% loss overall. Multiply the changes, don't add them: 1.10 × 0.90 = 0.99. To undo a 25% rise you need a 20% fall.
What is the difference between percent and percentage points?
Percentage points are the plain gap between two percentages. A rate that goes from 3% to 5% is up 2 percentage points, but that is a 66.67% increase in relative terms (2 ÷ 3 × 100). Use points for interest rates, tax rates and poll results.
How do I find the average percentage increase per year?
Divide the end value by the start value, take the root for the number of years, subtract 1 and multiply by 100. Growing from 1,000 to 1,500 in 5 years is 1.5^(1/5) − 1 = 8.45% a year. Simply dividing the 50% total by 5 gives 10%, which is too high.
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