Percentage Calculator
The three percentage operations people most often invert: percentage of a value, change between two values, and working backwards from a total.
Percentage Calculator
All calculations run instantly in your browser.
What is X% of Y?
X is what % of Y?
Percentage change from X to Y
Increase / Decrease Y by X%
X is X% more/less than what?
Part as % of Total
Percentage of a value
The straightforward direction — what is 15% of 240?
result = (percentage ÷ 100) × value
- percentage
- The rate, as a plain number (15 for 15%)
- value
- The base amount you are taking a share of
Worked example
- Percentage
- 15
- Value
- 240
- Calculation
- (15 ÷ 100) × 240
36
Percentage change between two values
The direction that causes arguments, because the answer depends entirely on which value is the baseline.
change % = ((new − old) ÷ old) × 100
- old
- The original value — the denominator, and the source of most errors
- new
- The value after the change
Worked example
- Old value
- 80
- New value
- 100
- Calculation
- ((100 − 80) ÷ 80) × 100
+25% increase
Going back the other way — 100 down to 80 — is a 20% decrease, not 25%. The denominator changed. This asymmetry is why a stock that falls 50% must rise 100% to recover.
Reverse percentage — finding the original
You know the figure after a percentage was applied and need the value before it. Subtracting the same percentage does not work.
original = final ÷ (1 + (percentage ÷ 100))
- final
- The amount you have, after the increase
- percentage
- The rate that was applied (use a negative value for a decrease)
Worked example
- Price including 20% VAT
- 120
- Calculation
- 120 ÷ 1.20
100 before VAT — the VAT portion is 20, not 24
Taking 20% off 120 gives 96, which is wrong by 4. The 20% was calculated on 100, not on 120, so it must be divided out rather than subtracted.
Percentage traps
Percentage points confused with percent
Cause:A rate moving from 4% to 5% is a rise of 1 percentage point — but a 25% increase. Reporting either number as the other misstates the change by a factor of 25.
Fix:Use "percentage points" for the arithmetic difference between two rates, and "percent" for proportional change. In finance the abbreviation is bps: 1 basis point = 0.01 percentage points.
Averaging percentages
Cause:A 50% gain followed by a 50% loss is not break-even — 100 becomes 150 then 75, a 25% loss overall. Percentages compound multiplicatively and cannot be averaged arithmetically.
Fix:Multiply the growth factors: 1.5 × 0.5 = 0.75. For an average rate over several periods, use the geometric mean, which is what CAGR computes.
Stacking discounts additively
Cause:"30% off, then a further 20% off" is not 50% off. 100 → 70 → 56, which is 44% off. The second discount applies to the already-reduced price.
Fix:Multiply the remaining fractions: 0.70 × 0.80 = 0.56. Sequential percentages always compound.
Applying a markup and reading it as a margin
Cause:Cost 60 marked up 66.7% gives a price of 100, but the margin is 40%. Markup is over cost; margin is over price. They are only equal at zero.
Fix:margin = markup ÷ (1 + markup). Confirm which denominator a stated percentage uses before pricing against it.
About
The Percentage Calculator solves the most common percentage problems: finding what percentage one number is of another, calculating a percentage of a number, computing percentage increase or decrease between two values, and reversing a percentage to find the original amount. Results update as you type.
How to use
- 1 Choose the calculation type from the tabs: % of Number, % Change, Ratio, or Reverse %.
- 2 Enter your numbers in the input fields.
- 3 The result is calculated and displayed instantly.
- How do I calculate what percentage one number is of another?
- Use the "% of Number" tab. Enter the part and the whole — the tool divides the part by the whole and multiplies by 100. For example, 45 out of 180 = (45 ÷ 180) × 100 = 25%. This is useful for exam scores, sales targets, and any ratio expressed as a percentage.
- How do I calculate percentage increase or decrease?
- Use the "% Change" tab. Enter the original value and the new value. The formula is ((new − original) ÷ original) × 100. A positive result is an increase; a negative result is a decrease. For example, from 80 to 100 is a 25% increase.
- What does Reverse % mean?
- Reverse % finds the original number before a percentage was applied. For example, if you know that 75 is 60% of a number, the reverse calculation gives you the original: 75 ÷ 0.60 = 125. This is useful for finding pre-tax prices, original prices before a discount, or base values in financial calculations.
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