Percentage Calculator

How it works

Select the calculation before entering the values. In X% of a value, the percentage is divided by one hundred and multiplied by the value. In One value as a percentage of another, the part is divided by the whole and multiplied by one hundred. Negative numbers are allowed for these arithmetic operations, but the whole cannot be zero: both a nonzero part divided by zero and zero divided by zero are shown as undefined. Percent means per hundred; the tool does not assume a percent sign entered in a basic number field.

Percentage change compares a final value with a positive starting value. It subtracts the start from the final value, divides by the start and multiplies by one hundred. The table keeps the absolute difference alongside the relative change. A starting value of zero makes the relative calculation undefined, and this tool also leaves it undefined for a negative start because a conventional growth percentage becomes difficult to interpret. The absolute difference is still available. This is an explicit reporting convention, not an assertion that division by a negative number is impossible.

Reverse a percentage change starts with the final value and the signed change that produced it. A positive percentage is an increase; a negative percentage is a decrease. The original is final divided by one plus the percentage divided by one hundred. If a final value of 80 followed a 20% decrease, enter 80 and −20: the original is 100. Adding 20% to 80 would produce 96 and does not undo the original decrease, because it uses a different base.

A −100% change is a special case. It multiplies every original by zero, so a zero final value cannot identify one unique original. A nonzero final value is incompatible with that change. The result explains the distinction. Changes below −100% remain valid signed arithmetic and reverse the sign; they should not be confused with an ordinary decrease of a nonnegative count. The tool supplies arithmetic, without interpreting a change as an investment return, tax rule or forecast.

Successive percentage changes takes a starting value and between one and one hundred signed changes separated by commas, semicolons or new lines. An optional trailing percent sign is accepted for each change in this list. Every step multiplies the previous result by one plus the current percentage divided by one hundred. It does not add the percentages together. The table records the result after each step, and net percentage change is available when the original starting value is positive. A zero or negative starting value can still be carried through the multiplications, but its relative net percentage is left undefined under the same convention used by Percentage change.

Percentage points mode treats the entered numbers as rates. It subtracts the starting rate from the final rate to obtain the point difference, then separately calculates the relative change if the start is positive. Enter 40 and 50, not 0.4 and 0.5, when your rates are 40% and 50%. A point difference retains the same scale as the entered rates and does not require division by the starting rate. That is why a rate moving from 0% to 5% has a five-point increase even though a relative increase from zero is undefined.

Use decimal points or exponent notation, without thousands separators. Each individual number is limited to forty characters. Non-finite input and overflowing results receive an error; long lists and empty list items are rejected instead of partially processed. Calculations use ordinary floating-point numbers, so they are not an exact decimal accounting system. Displayed ordinary values use up to twelve significant digits; scientific notation is used for very small or large values. CSV retains numeric results and explicit Undefined cells.

Changing an input or calculation clears the old result until you calculate again. Inputs stay in this page’s memory and are not stored or added to the URL. Copy and download preserve the explanation and calculation rows, helping you distinguish the entered assumptions from a rounded display value.

Common use cases

• Recovering a value before a known percentage change
• Checking several successive increases and decreases
• Distinguishing a percentage-point change from relative growth
• Explaining why a percentage change from zero is undefined
• Exporting a calculation and its intermediate results for review

Frequently asked questions

Standards and limitations

• Office for National Statistics: percentages and percentage points