Percentage Calculator

About Percentage Calculator

The Three Percentage Formulas

Every percentage calculation boils down to one of three formulas. This calculator handles all of them.

1. What is X% of Y?

Formula: Result = (Percentage / 100) x Number

Example: What is 15% of 240?

(15 / 100) x 240 = 0.15 x 240 = 36

Use this for calculating tips, taxes, discounts, commissions, and markups. If you want to find 20% of your monthly income to put into savings, this is the formula you need.

2. X is what percent of Y?

Formula: Percentage = (Part / Whole) x 100

Example: 45 is what percent of 180?

(45 / 180) x 100 = 0.25 x 100 = 25%

This is the formula teachers use for grading (you scored 38 out of 50, so your grade is 76%). It also works for figuring out what share of your budget goes to rent, or what proportion of survey respondents chose a particular answer.

3. Reverse percentage (find the original value)

Formula for increase: Original = Final / (1 + Percentage / 100)

Formula for decrease: Original = Final / (1 - Percentage / 100)

Example: A jacket costs £72 after a 10% discount. What was the original price?

£72 / (1 - 10/100) = £72 / 0.9 = £80

Reverse percentages are useful for working backwards from sale prices, figuring out pre-tax amounts, or finding the original value before VAT was added. The UK standard VAT rate is 20%, so to find the pre-VAT price of a £120 item: £120 / 1.20 = £100.

How to Calculate Percentage Change

Percentage change measures how much a value has increased or decreased relative to its starting point. The formula is:

Percentage Change = ((New Value - Old Value) / Old Value) x 100

Example: A stock price went from £50 to £65. The percentage change is:

((65 - 50) / 50) x 100 = (15 / 50) x 100 = 30% increase

If the price dropped from £50 to £42:

((42 - 50) / 50) x 100 = (-8 / 50) x 100 = -16% decrease

This comes up constantly in finance, business reporting, and data analysis. Year-on-year revenue growth, inflation rates, and investment returns are all expressed as percentage changes.

Quick Reference: Common Percentages

Percentage	As a Decimal	As a Fraction	Common Use
10%	0.10	1/10	Easy mental math base
12.5%	0.125	1/8	Common sales commission
15%	0.15	3/20	Standard US tip
20%	0.20	1/5	UK VAT rate
25%	0.25	1/4	Quarter - common fraction
33.3%	0.333	1/3	Splitting three ways
50%	0.50	1/2	Half
75%	0.75	3/4	Three quarters

Mental Math Tricks for Percentages

You don't always need a calculator. Here are shortcuts that work in your head:

• 10% of anything: move the decimal point one place left. 10% of 85 = 8.5
• 5% of anything: find 10% and halve it. 5% of 85 = 4.25
• 1% of anything: move the decimal point two places left. 1% of 85 = 0.85
• 15% tip: find 10% and add half of that. 15% of £60 = £6 + £3 = £9
• 20% tip/VAT: find 10% and double it. 20% of £60 = £6 x 2 = £12
• 25% of anything: divide by 4. 25% of 84 = 21
• The swap trick: X% of Y = Y% of X. So 8% of 50 = 50% of 8 = 4. This often makes the calculation much simpler.

That last trick is surprisingly useful. Next time you need 4% of 75, flip it: 75% of 4 = 3. Much easier.

Percentages in Everyday Life

Shopping: A "30% off" sale means you pay 70% of the original price. If a £50 shirt is 30% off, you pay £50 x 0.70 = £35. For more complex discount calculations, try the discount calculator.

Finance: Interest rates, inflation, tax brackets, and investment returns are all percentages. A savings account paying 4.5% AER on a £10,000 balance earns £450 per year before compounding. For compound growth over time, use the compound interest calculator.

Grades: Scoring 42 out of 50 on an exam gives you (42/50) x 100 = 84%. Most UK universities consider 70%+ a First, 60-69% an Upper Second (2:1), and 50-59% a Lower Second (2:2).

Business: Profit margins, markups, and ROI are percentage-based metrics. A 40% profit margin means £0.40 of every £1 in revenue is profit. See the profit margin calculator for detailed margin analysis.

Health: Body fat percentage, nutrient daily values, and medication dosages all use percentages. When a food label says "15% of your daily iron", that is based on the reference intake of 14mg for adults in the UK.

Percentage Points vs Percent: Why It Matters

This distinction trips up journalists, politicians, and professionals constantly. When a mortgage rate rises from 3% to 4%, there are two correct ways to describe it:

• 1 percentage point increase (the absolute change: 4 minus 3)
• 33.3% increase (the relative change: 1/3 of the original rate)

These describe very different things. A politician saying "unemployment dropped 2%" could mean it went from 6% to 4% (a 2 percentage point drop) or from 6% to 5.88% (a 2% relative drop). In financial contexts, the difference is enormous. If your savings rate goes from 2% to 4%, a "2 percentage point increase" doubles your interest income. A "2% increase" would only bump it to 2.04%.

Rule of thumb: when comparing rates, tax brackets, or other figures already expressed as percentages, use "percentage points" for the absolute difference and "percent" for the relative change.

Compound Percentage Changes

Percentages do not add up the way most people expect when applied sequentially. Two 10% drops do not equal a 20% total drop:

Scenario	Start	After First Change	After Second Change	Net Change
Two 10% drops	£1,000	£900	£810	-19% (not -20%)
Two 50% drops	£1,000	£500	£250	-75% (not -100%)
+20% then -20%	£1,000	£1,200	£960	-4% (not 0%)
+50% then -50%	£1,000	£1,500	£750	-25% (not 0%)

This asymmetry matters in investing. If your portfolio drops 50%, you need a 100% gain just to break even. A 33% drop needs a 50% gain to recover. This is why protecting against large losses matters more than chasing large gains.

The formula for combining sequential percentage changes is: Net change = (1 + r1) x (1 + r2) x ... - 1, where r values are expressed as decimals. For two 10% drops: (1 - 0.10) x (1 - 0.10) - 1 = 0.81 - 1 = -0.19 = -19%.

Markup vs Margin: The Business Confusion

These two terms are used interchangeably in casual conversation, but they produce different numbers from the same data. Getting them confused can wreck pricing decisions:

Term	Formula	Example (cost £60, price £100)	Result
Markup	(Price - Cost) / Cost x 100	(100 - 60) / 60 x 100	66.7%
Margin	(Price - Cost) / Price x 100	(100 - 60) / 100 x 100	40%

Same product, same numbers, but markup is 66.7% while margin is 40%. Markup is based on cost; margin is based on selling price. If your boss says "price it at a 40% margin" and you apply a 40% markup instead, you will sell a £60 item for £84 instead of £100 and lose money on every sale. For detailed margin analysis, the profit margin calculator handles both directions.

Percentages in Statistics: Margin of Error

When a news headline says "52% of voters support X, with a margin of error of plus or minus 3 percentage points", it means the real figure is likely between 49% and 55%. The margin of error comes from the sample size and confidence level of the poll.

At the standard 95% confidence level, common margins of error by sample size:

Sample Size	Margin of Error (95% confidence)
100	+/- 9.8 percentage points
400	+/- 4.9 percentage points
1,000	+/- 3.1 percentage points
1,500	+/- 2.5 percentage points
10,000	+/- 1.0 percentage points

This is why political polls with 1,000 respondents and a 3-point margin of error cannot reliably call a race where candidates are separated by 2 points. The results are within the margin of error and the race is genuinely too close to call from polling data alone. Notice also that quadrupling the sample size from 100 to 400 only halves the margin of error. The relationship follows a square root function: to cut the margin of error by half, you need four times as many respondents.

Common Mistakes to Avoid

• Adding percentages of different bases: A 10% increase followed by a 10% decrease does NOT get you back to the original. £100 + 10% = £110. £110 - 10% = £99. You lose £1.
• Forgetting the base: "Sales are up 200%" means sales tripled (the original plus 200% more). "Sales are 200% of last year" means sales doubled. The wording matters.
• Confusing "of" with "off": 25% of £80 = £20. 25% off £80 = £60. Small prepositions, big difference on a receipt.

For quick discount calculations when shopping, the discount calculator handles stacked discounts and tax. For compound growth over time (savings, investments), the compound interest calculator shows how percentages compound. And for business pricing with markup and margin, the profit margin calculator keeps the numbers straight.

All calculations run entirely in your browser. Nothing is sent to any server.

Sources

• GOV.UK - VAT rates (standard rate 20%)
• British Nutrition Foundation - UK Reference Intakes
• QAA - UK Degree Classifications
• Margin of Error - Statistical Reference
• Investopedia - Markup vs Margin
• BBC Bitesize - Percentages