Percentage Calculator

What This Percentage Calculator Does

A percentage is just a ratio expressed out of 100. The word comes from the Latin "per centum," meaning "per hundred," so 25% literally means 25 out of every 100. This tool handles the three percentage questions you actually run into day to day: finding a percent of a number, working out what percent one number is of another, and measuring the percent change between two values. Pick the mode that matches your question, enter your numbers, and the result updates as you type.

The Three Core Calculations

1. Finding a Percent of a Number

To find X% of Y, multiply Y by X and divide by 100. This is the math behind tips, discounts, sales tax, commissions, and interest. For example, 15% of 200 is 200 x 15 / 100 = 30. A 20% discount on an $80 item is 80 x 20 / 100 = $16 off, leaving a final price of $64. Because the operation is just multiplication, a percentage over 100 produces a result larger than the original: 150% of 40 is 60.

2. Working Out What Percent One Number Is of Another

Divide the part by the whole, then multiply by 100. If you answered 45 of 60 questions correctly, your score is 45 / 60 x 100 = 75%. If 18 of 24 seats in a room are filled, that is 18 / 24 x 100 = 75% occupancy. This is the right mode for test scores, survey results, completion rates, and any "X out of Y" situation.

3. Measuring Percent Change

Percent change compares a new value against an old one using the formula ((New - Old) / Old) x 100. The starting value is always the base you divide by. Going from 200 to 250 is a 25% increase, because the $50 gain is one quarter of the original 200. Going from 250 back to 200 is a 20% decrease, because the same $50 is now measured against the larger 250. That is why an increase and the matching decrease almost never share the same percentage.

Reverse Percentages: Finding the Original Amount

One of the most common real-world tasks is undoing a percentage to recover the original number. The key idea is to divide instead of multiply. If a receipt total of $120 already includes a 20% markup, the pre-markup price was 120 / 1.20 = $100. If a sale price of $80 reflects a 20% discount, the original ticket price was 80 / 0.80 = $100. A frequent mistake is adding the discount percentage back onto the sale price — adding 20% to $80 gives $96, not the true original of $100, because the discount was taken from a larger base.

Mental Math Shortcuts

• 10%: move the decimal one place left, so 10% of 240 is 24.
• 15%: take 10% and add half of it, so 15% of 240 is 24 + 12 = 36.
• 20%: double the 10% value, or just divide by 5.
• 25%: divide by 4; 50%: halve it; 5%: take half of 10%.
• Add or subtract: turn the percentage into a multiplier. To add 15%, multiply by 1.15; to remove 15%, multiply by 0.85.

Percentage vs. Percentage Points

These two phrases are easy to mix up but mean different things. When a rate moves from 5% to 8%, that is a 3 percentage point increase (the plain gap between the numbers) but a 60% relative increase (3 measured against the original 5). News coverage of interest rates, poll numbers, and unemployment often blurs the line, so it pays to ask whether a figure is a difference in points or a relative percent change before drawing a conclusion.

Common Mistakes to Avoid

• Dividing by the wrong base. Percent change always uses the old value, not the new one, as the denominator.
• Assuming a percentage increase and decrease cancel out. A 50% drop needs a 100% gain to recover, not another 50%.
• Stacking discounts by adding them. Two 20% discounts are not 40% off; applied in sequence they leave 0.80 x 0.80 = 64% of the price, a 36% total reduction.

When to Use a Different Calculator

This tool is built for general percentage math. If you are specifically figuring out a restaurant gratuity, the tip calculator adds per-person splitting. For sales tax on a purchase, a dedicated sales tax calculator applies the correct state rate. And for growth that compounds over many periods, such as savings or investments, a compound interest calculator handles the repeated percentage gains that a single percent-change figure cannot capture.