Percentage Calculator

Percentage Calculator

Use the calculator above to solve common percentage questions, including a percentage of a number, percentage increase or decrease, percentage change, reverse percentages, percentage difference, percentage points, discounts, tips, tax, markup, and grades.

Percentage formulas

The correct formula depends on the question you are asking:

• What is X% of Y? Multiply Y x (X / 100). For example, 15% of 200 is 200 x 0.15 = 30.
• X is what percent of Y? Divide the part by the whole and multiply by 100: (X / Y) x 100.
• Percentage increase or decrease: Subtract the original value from the new value, divide by the original value, then multiply by 100: ((new - original) / original) x 100.
• Reverse percentage: If a final value already includes an increase of X%, divide it by 1 + X / 100. For a decrease, divide by 1 - X / 100.
• Percentage difference: Compare two values without treating either as the starting value: absolute difference / average of the two values x 100.
• Percentage-point change: Subtract the old percentage from the new percentage. Moving from 20% to 25% is a 5 percentage-point increase, but a 25% relative increase.

Percentage change example

If a price rises from 80 to 100, the increase is 20. Divide 20 by the original value of 80 and multiply by 100. The result is a 25% increase. Reversing the values produces a 20% decrease because the comparison now starts from 100.

Avoid these common mistakes

• Use the original value as the denominator for percentage change.
• Do not confuse a relative percentage change with a percentage-point change.
• A 20% increase followed by a 20% decrease does not return to the starting value. For example, 100 becomes 120 and then 96.
• When the original value is zero, a standard percentage-change result is undefined because division by zero is not possible.

Related calculators

Use the discount calculator for sale prices, the markup calculator for pricing decisions, or the average calculator for arithmetic means.