Percentage Math Calculator

Calculate what X% of a value is, find what percentage one number is of another, or compute the percentage change between two numbers.

Result

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How to use this calculator

Pick the calculation type that matches the question you are trying to answer.
Enter X and Y. The labels on the inputs update with the mode so you always know which number goes where.
Read the result instantly — no submit button. The step-by-step working below the result shows exactly how the answer was derived.

About this calculator

A percentage is just a fraction with a denominator of 100, so every percentage problem reduces to a single multiplication or division. This calculator handles the three forms you actually run into in real life: finding a percentage of a value (sales tax, tip, discount), expressing one number as a percentage of another (test scores, conversion rates), and measuring percentage change between two values (price increases, growth rates). Each mode shows the step-by-step working underneath the result so you can check the math by hand or use the explanation to teach.

What this calculator does

This calculator answers the three percentage questions that come up most often in everyday math: (1) what is X% of Y — used for tax, tip, discount, and commission; (2) X is what percent of Y — used for test scores, conversion rates, and progress against a target; (3) percentage change from X to Y — used for price moves, growth rates, and margin shifts. Each mode shows the decimal conversion and the step-by-step working underneath the result so the math is reproducible by hand. The percentage-change mode divides by the absolute value of the original so the sign of the result tracks direction (up or down) rather than the sign of the base.

How it works — the formula

X% of Y = (X / 100) × Y
X is what % of Y = (X / Y) × 100
Percentage change = ((new − old) / |old|) × 100

Per-cent literally means "per hundred", so a percentage is a fraction with denominator 100. The three forms above cover the three questions people ask most often. For percentage change, dividing by |old| keeps the sign intuitive: a move from 100 to 80 is −20%, from 80 to 100 is +25%. Compound growth uses repeated multiplication by (1 + r), not addition of percentages.

Sources: NIST Engineering Statistics Handbook §1.3 — Measures of relative standing · Khan Academy — Intro to percentages · BLS Consumer Price Index methodology — percent change definitions

Worked examples

Example 1

What is X% of Y?

Inputs:: X = 25, Y = 200
Output:: 25% of 200 = 50

Example 2

X is what percent of Y?

Inputs:: X = 50, Y = 200
Output:: 50 is 25% of 200

Example 3

Percentage change

Inputs:: old = 80, new = 100
Output:: Change = +25.00% (use |old| in the denominator)

When to use this vs other tools

Percentage Calculator is the general-purpose tool. For dedicated retail, hospitality, or business-margin scenarios, the more specific tools below show the same math wrapped around a domain-specific input form.

Discount Calculator
Use when you have a list price and a percent-off and want the final price plus the dollar savings — same X% of Y math but with retail-friendly labels.
Tip Calculator
Use when splitting a restaurant check by tip percentage and number of diners — same X% of Y math plus a per-person divider.
Markup Calculator
Use when pricing inventory from cost — markup uses cost as the base (markup% = (price − cost) / cost), which is mathematically different from margin, even though both report a percent.
Profit Margin Calculator
Use when reporting profit as a percentage of revenue — margin uses revenue as the base (margin% = (revenue − cost) / revenue), not cost. Confusing the two is the most common percentage error in business.

Authority note

National Institute of Standards and Technology (NIST)

NIST SP 811 — Guide for the Use of the International System of Units (SI), §7.10.2 (the percent symbol)

NIST SP 811 §7.10.2 defines the percent symbol as the notational equivalent of "× 0.01" — i.e. the numeric form "X%" is exactly X / 100. The NIST Engineering Statistics Handbook §1.3 and the US Bureau of Labor Statistics CPI methodology give the same definitions for percent-of and percent-change used here.

Limitations

Percentages do not compose by simple addition — a 10% rise followed by a 10% fall returns to 99%, not 100%, of the start value.
A "percentage point" change differs from a "percent" change: an interest rate moving from 5% to 6% is up 1 percentage point but up 20 percent of the previous rate.
When the base is zero or negative, "percent change" is undefined or sign-ambiguous.
Use compound-interest formulas, not stacked percentages, when modeling growth over multiple periods.

Percentage math is exact arithmetic; rounding on display is for readability only. The full-precision value is used for any subsequent calculation.

Frequently asked

How do I calculate a percentage of a number?+

Convert the percentage to a decimal (divide by 100), then multiply by the number. For example, 25% of 200 is 0.25 × 200 = 50. Use the "What is X% of Y?" mode above for a worked example with any inputs you choose.

How do I figure out what percent one number is of another?+

Divide the first number by the second, then multiply the result by 100. For example, 50 out of 200 is 50 ÷ 200 = 0.25, which is 25%. Use the "X is what percent of Y?" mode above.

What is the formula for percentage change?+

Percentage change = ((new value − original value) ÷ |original value|) × 100. A positive result is an increase, a negative result is a decrease. The denominator uses the absolute value so the sign correctly reflects direction even when the original is negative.

Why does percentage change use the absolute value of the original?+

Using the absolute value keeps the sign of the result tied to whether the value went up or down, not to the sign of the original. Without it, going from −10 to −5 would compute as a negative change even though the value actually increased.

What is the difference between percentage points and percent?+

A percentage point is the arithmetic difference between two percentages — going from 5% to 7% is a 2-percentage-point change, but a 40% percent change. This calculator returns percent change for the third mode, not percentage points.

Can I use negative numbers?+

Yes — the calculator handles negative X or Y. The percentage change mode uses the absolute value of the original so direction (increase vs decrease) is reported correctly even with negative inputs.