Percentage Calculator Guide

A percentage expresses a number as a part of 100, which makes it easy to compare values of different sizes. People use percentages for discounts, tips, taxes, exam scores, price changes and business figures. This Percentage Calculator covers five common problems: finding a percentage of a number, finding what percent one number is of another, calculating percentage change, increasing or decreasing a value by a percentage, and finding the percentage difference between two values.

Each calculator box updates as you type, so there is no button to press. Results are rounded to a maximum of four decimal places.

Tip for Shoppers: "Buy 2, get 1 free" works out to about 33.33% off the price of the three items. Compare that with a flat 40% off sale to see which deal is better.

The Types of Percentage Problems

1. Finding the Percentage of a Number

Used for sales tax, tips, commissions and similar problems. For example, "What is 15% of $80?" The answer is $12.

2. Finding What Percent One Number is of Another

Used for scores, shares and proportions. For example, 25 out of 200 is 12.5%.

3. Percentage Change (Increase and Decrease)

Used for tracking growth, price changes and inflation. If a price goes from $100 to $120, that is a 20% increase. If it goes from $100 to $80, that is a 20% decrease. This is a directional measure, because it is calculated relative to the old (starting) value.

4. Increasing or Decreasing a Value by a Percentage

Used for discounts, markups and forecasts. To add 10% to 100, enter 10 and get 110. To apply a 20% discount to $50, enter −20 and get $40.

5. Percentage Difference (Scientific)

Used to compare two values when neither is the "original", for example in lab reports. It uses the average of both values as the base, so the result is the same whichever value you enter first. Comparing 50 and 75 gives a percentage difference of 40%. Going from 50 to 75 as a change, however, is a 50% increase. The two measures answer different questions. Both values must have the same sign; if one is positive and the other negative with an average of zero, the result is shown as N/A.

Standard Percentage Formulas

Percentage of a number: V = (P ÷ 100) × B

X as a percent of Y: P = (X ÷ Y) × 100

Percentage change: (New − Old) ÷ |Old| × 100

Increase / decrease: New = Old × (1 + P/100)

Percentage difference: |A − B| ÷ ((A + B) / 2) × 100

Where: V = value, P = percentage, B = base number. For a decrease, use a negative P.

How to Use This Calculator

Pick the box that matches your problem: for example "X is What % of Y" for a score, or "Percentage Change" for a price change.
Enter your numbers in both fields of that box.
Read the result: it appears immediately and updates as you edit the numbers.

Rule of 72: A common shortcut to estimate how long it takes to double money is to divide 72 by the annual percentage return. At 10% a year, money doubles in roughly 7.2 years. It is an approximation, not an exact figure.

The "Reverse" Trap: If a value falls by 50%, it needs a 100% gain just to get back to where it started. Percentage changes do not simply cancel each other out. You can check this with the Percentage Change box: 100 → 50 is −50%, but 50 → 100 is +100%.

Common Percentage, Decimal and Fraction Conversions

Percentage	Decimal	Fraction	Meaning
10%	0.1	1/10	One tenth
20%	0.2	1/5	One fifth
25%	0.25	1/4	One quarter
50%	0.5	1/2	Half
75%	0.75	3/4	Three quarters

Math Disclaimer: Percentages can be misleading when the base number is very small. A jump from 1 to 2 is a 100% increase even though the absolute change is only 1. Consider the actual values alongside the percentages. Do not rely on this tool alone for decisions about money, health or safety.

Math & Percentages: Frequently Asked Questions

How do I calculate a percentage increase?

Subtract the original number from the new number, divide the result by the original number, then multiply by 100. Or enter the old and new values in the Percentage Change box and it does this for you.

How do I calculate a discount?

Use the Increase / Decrease box with a negative percentage. For example, 20% off $50: enter 50 as the initial value and −20 as the percent change to get a final price of $40. The "Basic Percentage" box also shows the discount amount itself: 20% of 50 is $10.

Can a percentage be more than 100%?

Yes. A 100% increase means a value has doubled, and a 200% increase means it has tripled. For example, if profit grows from $1 million to $3 million, that is a 200% increase. A decrease, on the other hand, cannot go below −100%, which would mean the value fell to zero.

How do I turn a fraction into a percentage?

Divide the top number (numerator) by the bottom number (denominator) and multiply by 100. For example, 4/5 is 0.8, which is 80%. You can also enter 4 and 5 in the "X is What % of Y" box.

What is the difference between percentage change and percentage difference?

Percentage change measures how much a value moved from an old value to a new one, so the order matters (50 to 75 is +50%, 75 to 50 is −33.33%). Percentage difference compares two values against their average and does not depend on order (50 and 75 differ by 40% either way).

Why does a result show N/A?

N/A appears when the percentage cannot be defined: "X is what % of Y" when Y is 0, percentage change when the old value is 0, and percentage difference when the two values add up to zero.

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