Percentage Increase Calculator
Find the percentage increase or decrease between an old and a new value, or work forwards and backwards from a known percentage.
- Original value
- 100
- New value
- 125
- Absolute increase
- +25
- Multiplier (new ÷ original)
- × 1.25
Original vs new value
Step-by-step solution
Percentage increase = (New − Original) ÷ Original × 100
Step 1: Find the increase
Subtract the original value from the new value.
125 − 100 = 25
Step 2: Divide by the original value
25 ÷ 100 = 0.25
Step 3: Convert to a percentage
Multiply by 100.
0.25 × 100 = 25%
Step 4: Answer
25% increase
Need something else? Find a percentage of a number with the Percentage Calculator, a sale price with the Discount Calculator, growth over several years with the Compound Interest Calculator, or compare quantities with the Ratio Calculator.
Percentage increase measures how much a value has grown compared with where it started. Enter the original (old) value and the new value to calculate the percentage increase between two numbers; if the new value is lower, the calculator reports it as a percentage decrease instead. You can also work forwards (the new value after a 15% increase) or backwards (the original value before an increase), and compare signed percentage change with percentage difference.
Every answer comes with the absolute change, a bar comparison of the old and new values and a step-by-step solution that uses your numbers. For a percentage of a single number, such as 20% of 150, use the general Percentage Calculator.
How to Calculate Percentage Increase
To calculate the percentage increase between two numbers, compare the change with the value you started from. Take an old value of 80 and a new value of 100:
- Find the increase: subtract the original value from the new value. 100 − 80 = 20
- Divide by the original value: 20 ÷ 80 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
The value rose by 25%. If the result of step 1 is negative, the new value is smaller and the answer is a percentage decrease: 100 to 80 is a 20% decrease. The two numbers differ because each direction is measured from a different starting value.
Percentage Increase Formula
Percentage increase = (New value − Original value) ÷ Original value × 100
- Original value
- The old or starting value: last year’s salary, the price before the change, the first measurement.
- New value
- The value after the change.
- New − Original
- The absolute increase, in the same units as the values (money, people, visits).
- × 100
- Turns the decimal ratio into a percentage (0.25 becomes 25%).
Why divide by the original value?
A percentage increase answers “how much bigger is it compared with what it was?”, so the starting value is the reference point, or base. The same absolute change means different things at different starting points: going from 20 to 30 is a 50% increase, while 200 to 210 is only 5%, even though both went up by 10. Dividing by the new value instead would answer a different question and understate the growth.
For a fall in value, the matching formula is Percentage decrease = (Original − New) ÷ Original × 100. The original value can’t be 0: dividing by zero is undefined, so an increase from 0 has no percentage. Report the absolute change instead.
Percentage Increase Examples
Salary increase
Old salary 48,000 · new salary 52,800
(New − Original) ÷ Original × 100
52,800 − 48,000 = 4,800
4,800 ÷ 48,000 = 0.10
0.10 × 100 = 10%
10% raise
Product price increase
Old price 24.99 · new price 29.99
(New − Original) ÷ Original × 100
29.99 − 24.99 = 5.00
5.00 ÷ 24.99 = 0.2001
0.2001 × 100 ≈ 20.01%
≈ 20.01% price increase
Population growth
Population 84,000 → 91,560
(New − Original) ÷ Original × 100
91,560 − 84,000 = 7,560
7,560 ÷ 84,000 = 0.09
0.09 × 100 = 9%
9% population growth
Website traffic growth
Monthly visits 12,500 → 18,750
(New − Original) ÷ Original × 100
18,750 − 12,500 = 6,250
6,250 ÷ 12,500 = 0.5
0.5 × 100 = 50%
50% more traffic
Investment value growth
Portfolio 8,000 → 9,240
(New − Original) ÷ Original × 100
9,240 − 8,000 = 1,240
1,240 ÷ 8,000 = 0.155
0.155 × 100 = 15.5%
15.5% gain
Sales growth
Units sold 320 → 416
(New − Original) ÷ Original × 100
416 − 320 = 96
96 ÷ 320 = 0.3
0.3 × 100 = 30%
30% sales growth
Exam score improvement
Score 64 → 80 (out of 100)
(New − Original) ÷ Original × 100
80 − 64 = 16
16 ÷ 64 = 0.25
0.25 × 100 = 25%
25% improvement (16 percentage points)
Price after a 15% increase
Original price 200 · increase 15%
New = Original × (1 + % ÷ 100)
200 × 15 ÷ 100 = 30
200 + 30 = 230
or 200 × 1.15 = 230
New price 230
Percentage Increase vs Percentage Change
Percentage change is the general, signed measure: (new − old) ÷ old × 100. A positive result is a percentage increase, a negative one is a percentage decrease. So “a −20% change” and “a 20% decrease” say the same thing. This calculator names the direction for you so a fall is never reported as an increase.
Percentage difference is different again: it compares two values with no before or after (two shops, two measurements) by dividing the gap by their average, so the order doesn’t matter. And percentage of a number is a single-value calculation, such as 15% of 200, which the Percentage Calculator handles.
| Concept | Answers | Formula | Example |
|---|---|---|---|
| Percentage increase | How much did a value grow, relative to where it started? | (new − old) ÷ old × 100 | 80 → 100: +25% |
| Percentage decrease | How much did a value fall, relative to where it started? | (old − new) ÷ old × 100 | 100 → 80: 20% decrease |
| Percentage change | Which way and by how much did it move? (signed) | (new − old) ÷ |old| × 100 | 100 → 80: −20% |
| Percentage difference | How far apart are two values, with no before/after? | |a − b| ÷ ((a + b) ÷ 2) × 100 | 80 vs 100: 22.22% |
| Percentage of a number | What is p% of a value? | value × p ÷ 100 | 25% of 80 = 20 |
Percentage points are another trap: a rate moving from 10% to 15% rose by 5 percentage points, which is a 50% increase.
How to Calculate the New Value After a Percentage Increase
Multiply the original value by 1 plus the percentage as a decimal:
New value = Original value × (1 + Percentage ÷ 100)
A 15% increase on 200 is 200 × 1.15 = 230. A 20% increase multiplies by 1.20; a 20% decrease multiplies by 0.80.
Working backwards to the original value
To undo an increase, divide instead of subtracting:
Original value = New value ÷ (1 + Percentage ÷ 100)
If a price is 230 after a 15% increase, the original was 230 ÷ 1.15 = 200. Taking 15% off 230 gives 195.50, not 200, because 15% of 230 is larger than 15% of 200. Switch the calculator to “Original value” mode to do this for your numbers.
Common Uses of a Percentage Increase Calculator
Pay rises and job offers
Compare a new salary with the current one to see the real raise, or work out the salary after a promised percentage increase.
Prices and inflation
Measure how much a product, rent or bill went up. To remove a known increase from a price, use the original value mode rather than subtracting the percentage.
Business growth
Report month-over-month or year-over-year growth in revenue, sales, customers or sign-ups against the earlier period.
Website and social metrics
Track traffic, conversions or followers. A small base can make a modest change look huge, so show the absolute increase alongside the percentage.
Investments
Find the percentage gain or loss between the purchase value and the current value. For growth over several years, an annual (compound) rate is usually more useful.
Grades and performance
See how much a test score, time or personal best improved compared with the earlier result.
For growth over several periods, a single percentage increase hides the yearly rate; the Compound Interest Calculator and Inflation Calculator handle compounding. To mark up a cost price, use the Markup Calculator; for returns on money invested, the ROI Calculator.
How to Use the Percentage Increase Calculator
- Choose what you want to find: the percentage increase between two values, the new value after an increase, the original value before an increase, or the signed percentage change.
- Enter the two values. Decimals, negative numbers, thousands separators and currency symbols (such as $ or €) are accepted.
- Read the highlighted answer. A higher new value is labelled as an increase, a lower one as a decrease, and equal values as no change.
- Check the step-by-step solution, which uses your own numbers, and the bar comparison of the original and new values.
- If the original value is 0, the calculator explains why no percentage exists and shows the absolute change instead.
Frequently Asked Questions
How do you calculate percentage increase?
Subtract the original value from the new value, divide the result by the original value, then multiply by 100. From 50 to 75: 75 − 50 = 25, 25 ÷ 50 = 0.5, 0.5 × 100 = 50% increase.
What is the formula for percentage increase?
Percentage increase = (New value − Original value) ÷ Original value × 100. The original value is the base because the increase is measured relative to where the value started.
What is the difference between percentage increase and percentage change?
Percentage change is the general signed result of (new − old) ÷ old × 100. When it is positive it is a percentage increase; when it is negative it is a percentage decrease. A −20% change and a 20% decrease mean the same thing.
How do I calculate a 20% increase?
Multiply the original value by 1.20. For example, a 20% increase on 150 is 150 × 1.20 = 180. Equivalently, find 20% of 150 (30) and add it on.
How do I calculate the original value after an increase?
Divide the new value by 1 plus the percentage as a decimal. If a price is 230 after a 15% increase, the original was 230 ÷ 1.15 = 200. Subtracting 15% of 230 would give the wrong answer (195.50).
Can percentage increase be negative?
A negative percentage increase means the value went down, so it is really a percentage decrease. For example, going from 100 to 80 gives (80 − 100) ÷ 100 × 100 = −20%, which is a 20% decrease.
What happens if the original value is zero?
The percentage increase is undefined, because the formula divides by the original value and division by zero is not possible. No percentage of 0 can reach a positive number, so describe the change in absolute terms instead (for example, up from 0 to 100).
Can percentage increase be more than 100%?
Yes. A 100% increase means the value doubled; anything above that means it more than doubled. Going from 50 to 150 is a 200% increase, because the increase (100) is twice the original value.
Why is a 50% increase not undone by a 50% decrease?
Because the two percentages use different bases. 100 increased by 50% is 150, but 50% of 150 is 75, so a 50% decrease takes it to 75. Getting back to 100 needs a 33.33% decrease.
What is the difference between percentage points and percentage increase?
Percentage points are the plain difference between two percentages; percentage increase is that difference relative to the starting percentage. An interest rate rising from 4% to 5% is up 1 percentage point, which is a 25% increase.
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Last updated: September 29, 2026.