Percentage Calculator
Percentage FormulasSolve any percentage problem — find the part, the whole, or the percentage change.
Six instant percentage calculations — results update as you type.
Percentage of a number
What percentage?
Percentage change
Increase by percentage
Decrease by percentage
Find the whole
15% of 200 is 30.
Breakdown
- 1% of 200
- 2
- 15% of 200
- 30
- 200 minus 15%
- 170
- 200 plus 15%
- 230
Show your working
Assumptions
- Percentages are treated as exact decimal values, not rounded before the calculation.
- Results are displayed to a maximum of six significant decimal places.
- Percentage change uses the absolute starting value as the base, so a change from a negative number behaves predictably.
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Percentage facts
- How do you find a percentage of a number?
- Divide the percentage by 100, then multiply. 15% of 200 = (15 ÷ 100) × 200 = 30.
- How do you find what percentage one number is of another?
- Divide the part by the whole and multiply by 100. 30 is (30 ÷ 200) × 100 = 15% of 200.
- What is the difference between a percentage point and a percent change?
- A savings rate moving from 2% to 3% has risen by one percentage point, but that is a 50% increase in the rate itself.
- Why doesn’t a 20% fall then a 20% rise return to the start?
- Each change applies to a different base. £100 less 20% is £80; £80 plus 20% is £96, not £100.
Percentage Formulas
Basic Percentage
X% of Y = (X ÷ 100) × Y
Example: 15% of 200 = 0.15 × 200 = 30.
X is what % of Y = (X ÷ Y) × 100
Example: 30 is what % of 200? (30 ÷ 200) × 100 = 15%.
Percentage Change
Change = ((New − Old) ÷ Old) × 100
A positive result is an increase; negative is a decrease. Example: from 80 to 100 is +25%. The ROI calculator applies this formula to investment returns.
Increase / Decrease
Increase: New = Original × (1 + P/100)
Decrease: New = Original × (1 − P/100)
Increasing 200 by 15% gives 200 × 1.15 = 230. These formulas apply directly in the finance calculator for loan and savings scenarios.
Finding the Whole
Whole = Part ÷ (Percentage ÷ 100)
Example: 30 is 15% of what? 30 ÷ 0.15 = 200. For working with fractions and decimals alongside percentages, try the fractions calculator.
Worked example
Sale: item originally £80, now £60. Discount = ((80−60)÷80)×100 = 25% off. Tip: 18% of £47.50 = 0.18 × 47.50 = £8.55. VAT: price excluding 20% VAT is £120 — add VAT: 120 × 1.20 = £144. Reverse: £144 ÷ 1.20 = £120 (removing VAT from a gross price).
Related calculations
For the part-to-part form of the same arithmetic, use the ratio calculator, and the fractions calculator for the fractional form. Chances quoted as percentages are handled by the probability calculator.
Where Percentages Trip People Up
Percentage points are not percentages
If a savings rate moves from 2% to 3%, that is a rise of one percentage point — but a 50% increase in the rate itself. Both statements are true and they describe the same change. Headlines that say "rates rose 1%" when they mean one percentage point are technically wrong, and the difference matters whenever you compare rates, exam marks, poll results, or margins. The rule: a difference between two percentages is measured in percentage points; a change relative to the starting figure is measured in percent.
An increase and a decrease do not cancel out
Add 25% to £100 and you get £125. Take 25% off £125 and you get £93.75, not £100. The two percentages are applied to different bases — the first to £100, the second to £125 — so they never undo each other. To reverse a 25% increase you must divide by 1.25, not subtract 25%. This is the single most common percentage error, and it is why a "50% off, then 50% off again" sale is a 75% discount rather than a free item.
Stacked discounts multiply, they don't add
An extra 10% off an item already reduced by 20% is not 30% off. Each discount applies to the price after the previous one: 0.80 × 0.90 = 0.72, so you pay 72% of the original — a 28% total discount. The same multiplication works for any chain of changes, including price rises: two consecutive 10% increases give 1.10 × 1.10 = 1.21, a 21% rise rather than 20%.
Averaging percentages usually gives the wrong answer
Two shops each report a 10% and a 30% margin, so the average margin is 20% — only if both shops sell the same amount. Percentages describe ratios, and a ratio's average is only meaningful when the underlying bases are equal. To combine percentages correctly, work back to the absolute amounts, add those, then recalculate the percentage from the totals.
Everyday Percentage Tasks
Adding and removing VAT
UK VAT is 20% on most goods and services, with a reduced 5% rate on things like domestic energy. To add VAT, multiply the net price by 1.20. To strip VAT out of a gross price, divide by 1.20 — do not subtract 20%, which is the reversal error above and leaves you 4% short. On a £150 gross price the net is £125 and the VAT is £25, whereas subtracting 20% would wrongly give £120.
Tips and service charges
A 10–15% tip is customary in UK restaurants, and many bills already include a service charge of 12.5%, which you can ask to have removed. A quick mental method: 10% is the bill with the decimal point moved one place left, and half of that again gives you 15%. On a £62 bill, 10% is £6.20 and 15% is £9.30.
Sale prices and "was" pricing
To find the original price from a sale price and a discount, divide rather than multiply: an item at £48 after 40% off was 48 ÷ 0.60 = £80. This is the "find the whole" calculation above. It is also how you check whether a "was" price is genuine — UK guidance expects the higher price to have been the actual selling price for a meaningful period beforehand.
Marks, grades and weighted scores
A mark of 43 out of 70 is (43 ÷ 70) × 100 = 61.4%. Where components carry different weights, multiply each percentage by its weight before adding: coursework at 68% weighted 40% plus an exam at 55% weighted 60% gives (68 × 0.4) + (55 × 0.6) = 60.2%. Averaging 68 and 55 directly would give 61.5% and overstate the result.
Evidence & Methodology
How This Page Is Grounded
Method
Applies the standard part, whole, rate, percentage-change and reverse-percentage relationships for the selected mode.
Important limitation: Results depend on the meaning and units of the entered quantities; division by zero is rejected.
Primary Sources
- Understanding percent OpenStax
Quality Checks
All modes, zero values, negative change and reverse calculations are checked.
See how sources are selected and corrections are handled in our Editorial & Calculation Methodology, and which automated checks this page has to pass in How We Test.
Frequently Asked Questions
How do I calculate a percentage of a number?
To find X% of Y, use the formula (X ÷ 100) × Y — for example, 15% of 200 = 0.15 × 200 = 30. The percentage calculator above does this instantly as you type, with no button to press.
How do I calculate percentage change?
Percentage change is calculated as ((New − Old) ÷ Old) × 100 — a positive result is an increase, a negative result is a decrease. For example, from 80 to 100 is a +25% increase. Enter any two values in the percentage change calculator above to get the result instantly.
How do I find the original number when I only know a percentage and the part?
Use the formula: Whole = Part ÷ (Percentage ÷ 100). For example, if 30 is 15% of a number, then 30 ÷ 0.15 = 200. The "Find the whole" section of this percentage calculator handles this automatically.