How to Calculate a Percentage of a Number, Change and Difference

 

Percentage calculations depend on the question you are asking. Finding a percentage of a number, measuring a change from an original value, and comparing two values against their average use different formulas.

Use our Percentage Calculator to select the appropriate calculation and see its formula and reference value.

How do you calculate the percentage of a number?

Result = percentage / 100 x number.

For 15% of 240, divide 15 by 100 to get 0.15, then multiply by 240: the answer is 36. In Calculation mode, choose Percentage of a number, enter Percentage (%) 15 and Number 240, then select Calculate percentage. Enter 15 rather than 0.15 in the percentage field.

The portion is different from a new total after an increase or reduction. Adding 15% to 240 gives 240 + 36 = 276. Subtracting it gives 240 - 36 = 204. For a sale price, our Discount Calculator handles the remaining-price calculation.

Find what percent a part is of a whole

Percentage = part / whole x 100.

For 30 out of 150, 30 / 150 x 100 = 20%. Here, 150 is the reference. A whole of zero makes this division undefined.

A percentage can exceed 100%. For example, 150 is 150% of 100.

Calculate percentage change

Percentage change = (new - original) / original x 100.

From 80 to 100, the change is (100 - 80) / 80 x 100 = 25%, an increase. From 100 to 80, it is (80 - 100) / 100 x 100 = -20%, a decrease.

Reversing the values changes the denominator. That is why the increase and decrease are not equal-and-opposite percentages.

Calculate loss percentage

Loss percentage = (original - remaining) / original x 100.

If a value falls from 200 to 150, the lost amount is 50. Relative to the original 200, the loss is 25%.

The loss mode in our calculator accepts nonnegative values and a remaining value no higher than the original. A complete loss, from 200 to zero, is 100%. For an increase, choose Percentage change instead.

Percentage difference equation

When neither value is an original reference, a commonly used symmetric comparison uses their average:

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

For 80 and 100, the absolute difference is 20 and the average is 90. The result is 20 / 90 x 100, approximately 22.2222%. Reversing the inputs gives the same result.

This average-reference definition differs from percentage change and percent error against an accepted reference. Different fields can use different conventions. Check the definition required for your work.

Percentage points versus percent change

If a rate rises from 20% to 25%, the increase is 5 percentage points. Relative to the original rate, it is also (25 - 20) / 20 x 100 = 25%.

Those describe different comparisons. Do not report a five-point increase as a 5% relative increase.

Zero and negative values

A zero reference causes division by zero in a relative change or proportion. Our calculator reports an error rather than an invented finite percentage. For symmetric difference, two zero inputs also make the average denominator zero.

This version accepts nonnegative inputs only. Percentage change can still return a negative result when the new value is lower. Signed financial or scientific datasets may require a context-specific convention.

Common percentage mistakes

• Using the new value as the denominator for a change from the original.
• Treating symmetric difference as the same thing as increase or decrease.
• Confusing a percentage with a decimal fraction in the input field.
• Mixing percentage points and relative percentages.
• Adding successive price discounts instead of multiplying remaining-price factors.

For successive sale discounts and optional tax, use our Discount Calculator.

Frequently asked questions

Why does a 20% loss need a 25% gain to recover?

Starting with 100, a 20% loss leaves 80. Returning from 80 to 100 requires 20 / 80 x 100 = 25%. The reference changes.

Is percentage difference always below 100%?

No. Under the average-reference formula for nonnegative values, the result can reach 200% when one value is zero and the other is positive.

Does this tool calculate tax losses or investment returns?

No. It performs arithmetic on the entered values. It does not account for tax rules, cash-flow timing, fees, or financial reporting conventions.

Choose your percentage calculation

Open the Percentage Calculator, select the question you want to answer, and check the reference shown with the result.

This guide provides general arithmetic examples, not tax, financial, or statistical advice.