Percentage Calculator

Percentages show up everywhere — a tip, a discount, a tax rate, a grade, a pay rise — and almost every question takes one of three shapes. What is a given percent of a number? One number is what percent of another? And by what percent did a value change? This calculator answers all three from one panel, so you do not have to remember which formula applies.

The word percent simply means per hundred. Twenty percent is 20/100, or 0.2, and finding 20% of 80 is just 0.2 × 80 = 16. The skill that trips people up is the third case: percent change divides by the original value, not the new one. Going from 50 to 75 is a 50% increase, but going back from 75 to 50 is a 33.3% decrease, because the base changed.

That asymmetry matters in real decisions. A 20% discount followed by an additional 10% off is not 30% off; it is 28% off, because the second discount applies to the already-reduced price. Likewise, an investment that falls 50% needs a 100% gain just to break even. Understanding the base of the percentage is often more useful than the arithmetic itself.

Use the three-mode panel below for quick answers: type the numbers, and the result updates as you type. The formulas are listed underneath so you can reproduce any result by hand, and everything is computed in your browser, so nothing you enter is sent anywhere. If you are working through a homework problem or checking an invoice, start with the first mode — it is the one people need most often, and the other two modes are there when the question changes shape.

How the math works

Percent of: result = (percent ÷ 100) × value.
What percent: result = (part ÷ whole) × 100.
Percent change: result = ((new − old) ÷ old) × 100; positive means increase, negative means decrease.
Successive changes multiply: a 20% cut then a 10% cut is 0.8 × 0.9 = 0.72, i.e. 28% off, not 30%.

Frequently asked questions

How do I calculate a percentage of a number?

Divide the percent by 100 to get a decimal, then multiply. Fifteen percent of 200 is 0.15 × 200 = 30. Alternatively, move the decimal point two places left and multiply.

How do I work out a percentage increase?

Subtract the original from the new value, divide by the original, then multiply by 100. Going from 50 to 75: (75 − 50) ÷ 50 × 100 = 50%. The denominator is always the starting value.

Why is a 50% decrease not undone by a 50% increase?

Because each percentage is applied to a different base. Losing 50% of 100 leaves 50; gaining 50% of 50 gives 75, not 100. To recover a 50% loss you need a 100% gain.

Is 20% off then 10% off the same as 30% off?

No. The second discount applies to the reduced price, so the total is 1 − (0.8 × 0.9) = 28% off. Successive percentage changes multiply rather than add, which is why stacking discounts saves less than it appears.

What is the difference between percentage points and percent?

A change from 4% to 6% is a rise of 2 percentage points but a 50% increase. Percentage points describe the absolute difference between two percentages; percent describes the relative change.

Can this handle negative percentages?

Yes. Enter a negative percent to subtract, for example −12% of 500 is −60. Percent change also reports negatives, which indicate a decrease from the original value.

This calculator is an educational estimator. It is not financial, medical, tax, or legal advice, and it does not account for fees, local rules, or your personal circumstances. Confirm decisions with a qualified professional.

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How the math works

Frequently asked questions

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