Percentage Calculator: Of a Number, Change & Difference

 

Calculate a percentage of a number, a part as a percentage of a whole, percentage change, percentage loss, or the symmetric percentage difference between two values. Choose the mode that matches your question; each uses a different reference.

Choose your percentage calculation

This calculator accepts nonnegative inputs. Results include the formula and reference value. Changing modes clears inputs to avoid reusing numbers with a different meaning.

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How do you calculate the percentage of a number?

Result = percentage / 100 x number. For 20% of 150, enter 20 and 150: the result is 30. Enter percentages as 20, not 0.20, when you mean 20%.

Step-by-step example: what is 15% of 240?

  1. Divide the percentage by 100: 15 / 100 = 0.15.
  2. Multiply by the number: 0.15 x 240 = 36.
  3. In Calculation mode, select Percentage of a number. Enter Percentage (%) 15 and Number 240, then choose Calculate percentage.

The answer is 36. This is the portion, not the remaining amount after a reduction. To subtract 15% from 240, calculate 240 - 36 = 204. To add 15%, calculate 240 + 36 = 276.

How to calculate a percentage increase

Choose Percentage change: increase or decrease when comparing an original value with a new value. Subtract the original from the new value, divide by the original, then multiply by 100. A rise from 240 to 276 is (276 - 240) / 240 x 100 = 15%. The original reference must be greater than zero.

For worked examples and reference comparisons, read our guide to calculating a percentage of a number, change and difference.

What percent is one number of another?

Percentage = part / whole x 100. For 30 out of 150, the result is 20%. The whole must be greater than zero. A part larger than the whole gives a percentage above 100%.

Calculate percentage increase or decrease

Percentage change = (new - original) / original x 100. From 80 to 100, the increase is 25%. From 100 to 80, the decrease is 20%. Reversing the values changes the reference, so these are not equal-and-opposite percentages.

Loss percentage calculator

Loss percentage = (original - remaining) / original x 100. If an original value of 200 falls to 150, the loss is 50 / 200 x 100 = 25%. This mode requires an original greater than zero and a remaining value no higher than the original.

The loss mode is a relative-value calculation, not a tax-loss determination, investment return model, or deduction rule. For an increase, select Percentage change instead.

Percentage difference equation

Symmetric percentage difference = |first - second| / ((first + second) / 2) x 100.

For 80 and 100, the average is 90. The difference is 20 / 90 x 100, approximately 22.2222%. Reversing the inputs gives the same result. This differs from change measured against an original value.

We use this average-reference definition for nonnegative values. Different disciplines may define percentage difference or percent error differently. Check the required convention; both inputs zero make this formula undefined.

Frequently asked questions

What is a percentage point?

A move from 20% to 25% is an increase of 5 percentage points, but a relative increase of 25% because (25 - 20) / 20 x 100 = 25%. A relative percentage and a percentage-point difference are not interchangeable.

Can a percentage be over 100%?

Yes. For example, 150 is 150% of 100. A value can increase by more than 100%. In the nonnegative loss mode, loss cannot exceed 100%, because remaining value cannot be negative.

Why is a change from zero not calculated?

The original value is the denominator. Division by zero is undefined. A positive new value compared with zero does not have a finite relative percentage change under this formula.

Are negative inputs supported?

No. This version accepts nonnegative inputs to keep references unambiguous. A negative result is possible in Percentage change when the new value is lower than the original. If your dataset contains signed values, use the convention required for that context.

What inputs are supported?

Values from 0 to 1,000,000,000 with up to four decimal places. Use a decimal point or comma without thousands separators. Whole and original reference values must be greater than zero where required. All fields are mandatory for the selected mode.

Related calculator

For a sale price with successive percentage reductions and optional tax, use our Discount Calculator.

HandyMetric provides general arithmetic tools, not tax, financial, or statistical advice. Confirm that the selected formula matches the question you need to answer.

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