Percentage Calculator
Last Updated:
Seven percentage boxes in one place: a percent of a number, what percent one number is of another, percentage change, add or take off a percent, two kinds of reverse percentage, and percentage difference. Every answer shows the steps.
Quick answer: To find X% of Y, multiply Y by (X ÷ 100). To find what percent one number is of another, divide the part by the whole and multiply by 100. Example: 15% of $85 = (15 ÷ 100) × 85 = $12.75. This calculator also handles percentage change, adding or taking off a percent, reverse percentages and percentage difference.
How to Use the Percentage Calculator
Pick the box that matches your question
Each box answers one question: a percent of a number, what percent one number is of another, percentage change, add or take off a percent, two kinds of reverse percentage, or a percentage difference.
Enter your numbers
Type the values into the fields. A box shows a dash until every field has a value. If a value cannot be used, such as dividing by zero, the box tells you why.
Read the answer and the steps
The result updates as you type, with the steps shown underneath so you can check the answer by hand.
Use Clear to start over
The Clear and Start Over button empties all seven boxes and returns the cursor to the first field.
Percentage formulas for the seven common questions
Percentages turn up in discounts, sales tax, tips, pay raises, test scores and interest rates. The seven boxes above cover the most common percentage questions, from "what is 3.6% of 1,658" to "what was the price before a 20% discount". Each box shows the steps under the answer, so you can check the calculation by hand or copy the method into a spreadsheet.
📐 Core Percentage Formulas
How do you calculate a percentage of a number?
Divide the percentage by 100, then multiply by the number. To find a 20% tip on a $64 bill, calculate 0.20 × 64 = $12.80. That is the same calculation behind a restaurant tip, a sales tax charge, a sales commission or any percentage of an amount of money. Use the first box above and the steps appear under the answer.
A harder one: 3.6% of 1,658 is 0.036 × 1,658 = 59.688, or about 59.69. The percentage does not have to be a whole number, and the amount can be a count, a weight or a score.
How do you find what percent one number is of another?
Divide the part by the whole, then multiply by 100. If you scored 43 out of 60 on a test, 43 ÷ 60 × 100 = 71.7%. The same calculation answers "what is X as a percentage of Y" for a percentage of marks, a grade, a completion rate or a budget share: 38 out of 50 points is 76%. If you are calculating a course grade, the final grade calculator weights each assignment for you.
How do you calculate percentage change?
Subtract the old value from the new value, divide by the old value, then multiply by 100. That is the percentage change between two numbers. A price that rises from $80 to $92 changed by (92 − 80) ÷ 80 × 100 = 15%. A positive answer is an increase and a negative answer is a decrease.
The same calculation works for pay. A salary that goes from $52,000 to $55,640 is up 7%, because the $3,640 raise is 7% of $52,000. Always divide by the old value. Dividing by the new one understates increases and overstates decreases. The calculator asks for a positive old value, because a percentage change from a negative starting point reads backward.
How do you add or take off a percentage?
Multiply by 1 plus the rate to add, or by 1 minus the rate to take off. A $250 item with 8% sales tax costs 250 × 1.08 = $270. A $120 jacket at 25% off costs 120 × 0.75 = $90. A 4% pay raise on $60,000 gives 60,000 × 1.04 = $62,400. If you are calculating a sale price, the discount calculator is built for it.
How do you work backwards with a reverse percentage?
Divide the final amount by 1 plus the rate if a percentage was added, or by 1 minus the rate if one was taken off. A jacket costs $63 after 30% off, so the original price was 63 ÷ 0.70 = $90. A total of $120 that includes 20% tax came from 120 ÷ 1.20 = $100 before tax, which means $20 of it is tax.
Do not take 20% off $120. That gives $96, which is wrong because the 20% was worked out on the smaller number, not on the total. The same math covers VAT, GST and sales tax.
The other reverse question is "X is P% of what number?" If 45 is 30% of a number, divide 45 by 0.30 to get 150. With no calculator, find 1% first: if $63 is 70% of the original, 1% is $0.90, so 100% is $90.
What is the difference between percentage difference and percentage change?
Percentage change has a starting point. It measures how far a value moved from where it began. Percentage difference compares two numbers when neither one is the starting point, such as the prices of two phones or two lab readings. It divides the gap by the average of the two, so it works for any two values of 0 or more, as long as they are not both 0. For 40 and 50, the gap is 10, the average is 45 and the difference is 22.2%. The change from 40 to 50 is 25%.
What is the difference between a percentage point and a percent?
Percentage points describe the gap between two percentages. A percent describes the relative change. If an interest rate moves from 5% to 7%, that is a 2 percentage point rise, but the rate itself went up 40% (2 ÷ 5 = 0.40). The two are often confused. To find the percentage change between two percentages, enter them as plain numbers in the percentage change box.
Why an 8% rise followed by an 8% cut does not cancel out
Take a $1,200 monthly salary. An 8% raise makes it 1,200 × 1.08 = $1,296.00. An 8% cut on the new figure makes it 1,296 × 0.92 = $1,192.32. That is $7.68 below where you started, a net change of −0.64%. The cut is worked out on the larger amount, so it removes more dollars than the raise added. Equal percentage rises and falls only cancel out at 0%.
Quick mental math for common percentages
- 10%: Move the decimal point one place left. 10% of $347 = $34.70
- 5%: Half of 10%. 5% of $347 = $17.35
- 20%: Double the 10% figure. 20% of $347 = $69.40
- 15%: Add 10% + 5%. 15% of $347 = $34.70 + $17.35 = $52.05
- 25%: Divide by 4. 25% of $80 = $20
- 1%: Move decimal two places left. 1% of $3,400 = $34
Common real-world percentage calculations
| Situation | Calculation | Example |
|---|---|---|
| Sales discount | Original × (1 − discount%) | $200 × 0.85 = $170 (15% off) |
| Tax added | Price × (1 + tax%) | $50 × 1.08 = $54 (8% tax) |
| Price before tax | Total ÷ (1 + tax%) | $54 ÷ 1.08 = $50 (8% tax) |
| Pay raise | Salary × (1 + raise%) | $72,000 × 1.05 = $75,600 (5% raise) |
| Tip calculation | Bill × tip% | $85 × 0.20 = $17 tip |
| Investment return | ((End − Start) ÷ Start) × 100 | ($12,000 − $10,000) ÷ $10,000 = 20% |
| Grade score | (Correct ÷ Total) × 100 | (38 ÷ 50) × 100 = 76% |
How do you calculate a percentage in Excel or Google Sheets?
Both programs use the same formulas, such as =A1*B1 for a percent of a number. Put the values in cells A1 and B1, then format the result cell as a percentage when the answer is a percent. Type a rate such as 8% into its cell as 8% or 0.08, never as 8.
| Task | Formula | Example |
|---|---|---|
| A percent of a number | =A1*B1 | A1 = 240, B1 = 15% gives 36 |
| One number as a percent of another | =A1/B1 | A1 = 19, B1 = 25 gives 76% |
| Percentage change | =(B1-A1)/A1 | A1 = 200, B1 = 250 gives 25% |
| Add a percentage | =A1*(1+B1) | A1 = 300, B1 = 8% gives 324 |
| Take off a percentage | =A1*(1-B1) | A1 = 160, B1 = 25% gives 120 |
| Original before a rise | =A1/(1+B1) | A1 = 150, B1 = 20% gives 125 |
Does the calculator work for UK, Australian and Canadian tax?
Yes, for the arithmetic. The calculator does not know any country's rates or rules, so you enter the rate yourself. The US adds sales tax at the register, the UK charges VAT and Australia charges GST. Canada charges GST, which some provinces combine into HST (Ontario is the usual example), while others add a provincial sales tax on top. Shop prices in the UK normally include VAT already, so the reverse box that finds the original value is the quick way to get the amount before tax.
Common percentage mistakes
- Dividing a change by the new value instead of the old one.
- Adding percentages that apply to different amounts. Two 10% rises in a row make 21%, not 20%, because 1.10 × 1.10 = 1.21.
- Treating a percentage point and a percent as the same thing.
- Reversing a discount by adding the same percentage back. $100 less 20% is $80, and 20% on top of $80 is $96, not $100.
Frequently Asked Questions
Sources & Methodology
This page uses standard arithmetic, not published rates or statistics, so there is no outside data to cite. Every formula is shown with a worked example, and each answer shows its steps so you can check it by hand. Percentage difference divides the gap between two values by their average. The prices, salaries and tax rates in the examples are illustrations, not current rates or advice.