Percentage calculator with formulas
Six everyday calculations as you type: percent of a number, percentage of a total, percentage change, increase or discount, original value and successive changes, with the formula.
Change the numbers: the result and the calculation update as you type.
Percent of a number
What is % of ?
Percentage of a total
is what percent of ?
Percentage change
From to , what is the percentage change?
Increase or discount
by %
Original value
After a of %, the result is . What was the original value?
Successive changes
A change of % then %: what is the overall change?
Use a point for decimals and “−” or “-” for a decrease. Results are rounded as you choose, with “≈” when the exact value has more decimals. Everything is worked out in your browser: nothing is sent.
Work out any percentage in seconds
Change the numbers in any of the six boxes: the result appears as you type, along with the calculation done on your numbers. The calculator answers the most common questions:
- what is 20% of 150 (percent of a number);
- 30 is what percent of 150 (a share, a test score, a success rate);
- how much a value went up or down, as a percentage (percentage change);
- the price after a discount or an increase of x%;
- the original value, for example the price before a sale;
- the total of two successive changes, which don’t simply add up.
You choose the rounding, from whole numbers to four decimal places, and one click copies the result. It’s free, with no sign-up, and everything is worked out in your browser.
Percentage formulas
A percentage is a fraction of 100: 20% means 20 out of 100, or 0.2. Every formula follows from that.
| What you want | Formula | Example |
|---|---|---|
| x% of a number | number × x ÷ 100 | 20% of 150 = 30 |
| Percentage of a total | part ÷ total × 100 | 30 out of 150 = 20% |
| Percentage change | (new − old) ÷ old × 100 | from 80 to 100 = +25% |
| Increase by x% | value × (1 + x ÷ 100) | 150 + 20% = 180 |
| Decrease by x% | value × (1 − x ÷ 100) | 80 − 25% = 60 |
| Value before an x% decrease | final value ÷ (1 − x ÷ 100) | 60 after −25%: 80 to start with |
A mental math tip: 10% of a number is the number divided by 10. 10% of 80 is 8, so 5% is 4 and 15% is 12.
The multiplier
Increasing by 20% means multiplying by 1.2; taking 25% off means multiplying by 0.75. That number is the multiplier: 1 + x ÷ 100 for an increase, 1 − x ÷ 100 for a decrease. It makes every calculation simpler.
- To chain two changes, multiply the multipliers. A 30% sale followed by an extra 20% off gives 0.7 × 0.8 = 0.56: the price is down 44%, not 50%.
- To go back, divide by the multiplier. An item that costs $42 after 30% off was $42 ÷ 0.7 = $60.
Discounts, tax and tips: examples
- Sale price: a $59 jacket with 30% off costs 59 × 0.7 = $41.30. You save $17.70.
- Sales tax: with an 8% sales tax, a $50 item costs 50 × 1.08 = $54.
- VAT in the UK: at 20%, the price including VAT is the net price × 1.2. To remove VAT, divide by 1.2: £120 including VAT is £100 net. Taking 20% off £120 would give £96, which is wrong.
- Tip: a 20% tip on a $45 bill is 45 × 0.2 = $9.
- Test score: 45 out of 50 is 45 ÷ 50 × 100 = 90%.
Common percentage mistakes
- +10% then −10% doesn’t bring you back. 100 up 10% is 110, and 110 down 10% is 99: −1% overall (1.1 × 0.9 = 0.99).
- A 50% drop takes a 100% rise to recover, not 50%: 100 → 50 → 100.
- Percent and percentage points are not the same. An interest rate that goes from 3% to 4% rises by 1 percentage point, but by about 33%.
- An increase can be more than 100% (a price that triples has gone up 200%), a decrease never: beyond −100%, nothing is left.
Need help with math?
To understand an exercise or a method, Nation’s assistants can help:
- Hakim explains and solves math problems, step by step;
- the number to words converter writes an amount out in words, for a check or a contract.
Frequently asked questions
How do you calculate a percentage of a number?
Multiply the number by the percentage, then divide by 100. 15% of 80 is 80 × 15 ÷ 100 = 12. In your head, start from 10% (the number divided by 10): 10% of 80 is 8, and 5% is 4.
How do you calculate the percentage between two numbers?
Divide the part by the total, then multiply by 100. 45 out of 60 is 45 ÷ 60 × 100 = 75%. That’s how you turn a score, a success rate or a share of a budget into a percentage.
How do you calculate a percentage increase or decrease?
Work out (new value − old value) ÷ old value × 100. From 1,800 to 1,890 is +5%; from 250 to 200 is −20%. The result is positive for an increase and negative for a decrease.
How do you calculate a 30% discount?
Multiply the price by 0.7, which is 1 − 30 ÷ 100. A $59 item costs $41.30 after a 30% discount, a saving of $17.70.
How do you find the original price before a discount?
Divide the sale price by the multiplier. An item at $42 after 30% off was $42 ÷ 0.7 = $60. Adding 30% to $42 would give $54.60, which is wrong.
How do you add or remove sales tax or VAT?
To add it, multiply by 1 + the rate: $50 plus 8% sales tax is 50 × 1.08 = $54. To remove it, divide by the same number: £120 including 20% VAT is 120 ÷ 1.2 = £100.
Why doesn’t +10% then −10% bring you back to the start?
Because the decrease applies to a bigger amount. 100 + 10% = 110, then 110 − 10% = 99. With multipliers: 1.1 × 0.9 = 0.99, so −1% overall. The successive changes calculator does this for you.
What is the difference between percent and percentage points?
Percentage points measure the gap between two rates; percent measures the change. A rate that goes from 3% to 4% is up 1 percentage point, but it has increased by about 33%.
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