Free number tools · Know your baseline
Four common percentage questions, with the formula and baseline made clear. Find a percentage, compare two values, calculate a change or recover the original value.
Your values are calculated on your device. This tool does not upload or save your numbers. Refreshing or switching languages clears them. The site uses Google Analytics for page visits.
Enter two values, then calculate.
Includes the question, normalized inputs, formula, baseline, result and precision. Editing a value or option clears the old result; calculate again to update it.
Percentage change describes the change relative to where you started: (new − original) / original × 100. Using the new value would answer a different question. An increase from 80 to 100 is 25%; a decrease from 100 to 80 is 20%. The same change in amount can have a different percentage because the baseline changed.
Choose Reverse percentage, enter the final price, enter the percentage taken off, and choose Decrease. Divide the final value by 1 − rate / 100. For example, 90 / (1 − 10 / 100) = 100. Adding 10% to 90 gives 99, because that uses a different baseline.
For a prior increase, choose Increase and divide by 1 + rate / 100 instead. Open University: reverse percentages
The calculation is exact for the numbers you enter, but a displayed price or rate may already have been rounded. If that information was lost, the recovered original is an estimate, even when its computed decimal terminates. Multiple original amounts can round to the same final price. Keep full precision during calculation and apply the relevant rounding rule only at the end.
0% of a value is 0, and 0 as a part of a positive whole is 0%. A zero whole cannot be a denominator. Percentage change from an original value of 0 is undefined, including 0 to 0; a positive value falling to 0 is a −100% change.
After a 100% decrease, every nonnegative original becomes 0, so 0 cannot reveal a unique original. A nonzero final value is incompatible with that decrease. Reverse decreases of 100% or more are rejected.
No. A rate moving from 10% to 12% rises by 2 percentage points. Relative to the original rate of 10%, that is a 20% increase: (12 − 10) / 10 × 100 = 20%. To calculate that relative change here, enter 10 and 12 in Percentage change. The raw change is 2; those units are percentage points when the inputs are rates.
Yes. 150% of 80 is 120. A part of 30 compared with a whole of 20 is 150%. Going from 20 to 50 is a 150% increase. These inputs are supported. The exception is a reverse decrease: this tool accepts only nonnegative values, so the decrease must be below 100% to recover a unique original.
Decimal inputs are kept as exact fractions using integer arithmetic. Only the displayed result is rounded, to at most 0, 2, 4, 8 or 12 decimal places. Rounding is half up, with ties away from zero; trailing zeros are omitted. The default is 8 places.
≈ marks any loss of precision, including a tiny nonzero result shown as ≈ 0. One third as a percentage is ≈ 33.33333333%; its exact value is (100 / 3)%. Open Exact details to see the fraction and, when it terminates, the full decimal. A repeating decimal is never labeled an exact finite decimal.
Use nonnegative decimal numbers, such as 15, 0.5 or .5. Enter 15 for 15%. Do not include signs, commas, currency symbols, a % sign or scientific notation. Surrounding whitespace is allowed. Each input is limited to 128 characters after trimming and 4096 characters before trimming.
Each mode keeps its own draft while this page stays open. Switching modes restores that mode’s draft and clears the old result; the same numbers are not silently reused for a different question. Examples fill only empty fields. Clear empties the current mode. Editing any value or option clears the result until you calculate again.
Calculations run on your device. This tool does not upload your numbers, store them in browser storage or add them to the address. Refreshing the page or switching languages clears the drafts. Copy summary includes the question, normalized inputs, formula, baseline, result and display precision. The site uses Google Analytics for page visits.
The question behind this tool: find the original price after a discount