To calculate a percentage of a number, multiply the number by the percent and divide by 100 (or multiply by the decimal form: 20% is 0.20).
To calculate a percentage of a number, multiply the number by the percent and divide by 100 (or multiply by the decimal form: 20% is 0.20). Percentage change is (new − old) ÷ old × 100. A reverse percentage finds the original amount before a percent was applied. Those three ideas cover tips, discounts, exam scores and UK VAT.
Below you will find formula tables, worked examples (including UK 20% VAT) and common pitfalls such as stacking discounts. For quick answers, use the percentage calculator. For shop pricing try the discount calculator and the VAT calculator.
If you prefer to avoid hand arithmetic, the calculators on this site mirror the formulas below exactly, so you can cross-check school homework, invoices or tip splits.
Across school exams, shop floors and finance teams, the same six formulas appear again and again. Learn them once in plain language and you can audit any calculator output, including the ones linked here.
Contents
| Task | Formula | Example |
|---|---|---|
| Percentage of | part = whole × (percent ÷ 100) | 20% of 80 = 16 |
| What percent | percent = (part ÷ whole) × 100 | 16 is what % of 80? → 20% |
| Percentage change | ((new − old) ÷ old) × 100 | 80 → 100 = +25% |
| Increase by % | new = old × (1 + percent/100) | 80 increased by 25% = 100 |
| Decrease by % | new = old × (1 − percent/100) | 80 decreased by 25% = 60 |
| Reverse % (find original) | original = final ÷ (1 + percent/100) | After +20%: 120 → 100 |
Write percents as decimals when you multiply: 5% = 0.05, 12.5% = 0.125, 100% = 1. People trip up when they divide by the wrong base, especially for percentage change. Always divide by the starting value, not the ending value, unless you are answering a different question on purpose.
Mental maths shortcuts help day to day: 10% is the number with the decimal point moved one place left; 5% is half of that; 1% is the decimal moved two places. Build other percents from those blocks (15% = 10% + 5%).
Teachers often ask for answers to a set number of decimal places. For money, use two decimal places. For scientific work, follow the precision stated in the question. Do not round intermediate steps more tightly than your final display unless a method requires it.
Print the table or keep it nearby until the patterns feel automatic. Most day-to-day problems are a remix of those six rows.
Fractions and percents convert both ways: 1/4 = 25%, 3/5 = 60%, and 0.125 = 12.5%. Being fluent in those conversions speeds up estimation when a calculator is out of reach.
Estimating before calculating catches wild mistakes. If you need 19% of 400, you know 20% is 80, so the answer sits near 76. When a spreadsheet returns 760, you immediately suspect a missed decimal.
Example: what is 20% of £80? Compute 80 × 0.20 = 16. So 20% of £80 is £16. Example: what is 12.5% of £48? Compute 48 × 0.125 = 6. That is a common UK restaurant tip style amount when no service charge appears on the bill.
Example: a test score of 46 out of 50. Percent = (46 ÷ 50) × 100 = 92%. Example: 3 out of 8 as a percent is (3 ÷ 8) × 100 = 37.5%.
When the "whole" changes over time (population, revenue, followers), say which whole you used. "10% of customers" means nothing if the customer count is unclear.
Try the same inputs in the percentage calculator to confirm your arithmetic on awkward decimals.
Weights and cooking scale the same way: 60% of a 500g flour bag is 300g. Sports win rates are wins ÷ matches × 100. Once you see the pattern, the hard part is naming the whole correctly.
Business dashboards often show "percent of total" for categories. Sort categories by that share when you want a Pareto-style view of what dominates the whole.
Markups and margins use related percent language but different bases. A 25% markup on cost multiplies cost by 1.25. A 25% margin on selling price means cost is 75% of the sell price. Confirm which base your industry uses before you automate a formula.
Percentage change answers "how different is the new value relative to the old one?" From 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase. From 100 to 80: (80 − 100) ÷ 100 × 100 = −20% (a 20% decrease). Notice the asymmetry: up 25% then down 20% returns to the start only for this pair of numbers because the bases differ.
Salary example: £30,000 to £33,000 is a 10% rise. Price example: a £250 phone on sale for £200 falls by 20%. Always keep the sign in mind when you report change in dashboards: a negative change is a decrease.
Compound changes multiply. A 10% rise followed by another 10% rise is ×1.1 ×1.1 = ×1.21, which is a 21% rise from the start, not 20%. The same idea applies to percentage decreases: two successive 10% cuts leave 81% of the original (×0.9 ×0.9), a 19% total fall.
Inflation and investment returns are usually quoted as percent changes over a period. Comparing them still requires the same starting-base discipline. A chart that re-bases to 100 at the start makes relative moves easier to read.
Month-over-month and year-over-year changes are still percentage change; only the window differs. Label the window so readers do not compare a monthly move to an annual one by accident.
Index numbers ("rebased to 100") are percentage-change cousins. If an index moves from 100 to 108, that is an 8% rise from the base period. Reading the base date on a chart matters as much as reading the last point.
Reverse percentage problems give you the result after a percent change and ask for the original. If a price including a 20% increase is £120, the original is 120 ÷ 1.20 = £100. If a discounted price is £80 after 20% off, the original is 80 ÷ 0.80 = £100.
The key is to express the final amount as original × factor. For an increase of p%, factor = 1 + p/100. For a decrease of p%, factor = 1 − p/100. Divide the final amount by that factor.
A common exam trap: "a jumper costs £36 after 10% off; find the original." Students sometimes compute 36 × 1.10, which is wrong. The correct reverse is 36 ÷ 0.90 = £40.
Another trap is reversing a percent of a percent without resetting the base. Work one step at a time and write the factor for each step.
Shop labels sometimes show "was / now" prices. You can verify the claimed percent off with percentage change from the was price to the now price. Trading-standards rules on reference pricing vary by country; the maths still uses the same formulas.
Tax-inclusive wages and list prices use reverse percentages constantly. Write the factor on paper before you divide so you do not flip add and remove.
Salary sacrifice and deductions can look like reverse percentages when you only see the net figure. Still, employment payslips mix tax rules with percents, so treat payslip reconstruction carefully and use official calculators for tax.
Tip: on a £48 bill at 12.5%, tip = 48 × 0.125 = £6. Total = £54. Discount: 30% off a £70 item is 70 × 0.30 = £21 off, so you pay £49. You can also compute the pay price directly: 70 × 0.70 = £49.
UK VAT at 20%: standard-rated goods add 20% on the net price. Net £100 → gross £120. To extract VAT from a VAT-inclusive figure: VAT = gross × (20/120) = gross ÷ 6. So £120 includes £20 VAT and £100 net. To add VAT: gross = net × 1.20. To remove VAT: net = gross ÷ 1.20.
| Scenario | Input | Working | Result |
|---|---|---|---|
| 20% of £250 | 250 | × 0.20 | £50 |
| Add 20% VAT | net £250 | × 1.20 | £300 gross |
| Remove 20% VAT | gross £300 | ÷ 1.20 | £250 net |
| VAT portion only | gross £300 | ÷ 6 | £50 VAT |
| 15% off £80 | 80 | × 0.85 | £68 to pay |
Stacking discounts is not the same as adding the percents. 20% off then 10% off means ×0.8 ×0.9 = ×0.72, so 28% off in total, not 30%.
For checkout maths, try the discount calculator for off-price problems. VAT-inclusive and exclusive totals belong in the VAT-focused workflow on the same site tools list in the introduction.
Service charges on restaurant bills are often 12.5%. Treat them like any other percent of the net food and drink total unless the menu says otherwise.
Reduced and zero VAT rates exist for some UK goods and services; the arithmetic for those rates uses the same structure with a different percent. Always confirm the correct rate for the item before you invoice.
Example walk-through: a net consulting fee of £850 with 20% VAT. Gross = 850 × 1.2 = £1,020. VAT = £170. If the client quotes £1,020 inclusive, net = 1020 ÷ 1.2 = £850. Same numbers, opposite direction.
In Excel or Google Sheets, store 20% as 0.2 and format the cell as a percent, or type 20% directly. A cell formula for percentage of is =A1*B1 when B1 holds 0.2. Percentage change is =(new-old)/old.
In Python:
def pct_of(whole, percent):
return whole * (percent / 100)
def pct_change(old, new):
return (new - old) / old * 100
def reverse_increase(final, percent):
return final / (1 + percent / 100)
print(pct_of(80, 20)) # 16.0
print(pct_change(80, 100)) # 25.0
print(reverse_increase(120, 20)) # 100.0Floating-point rounding can leave values such as 19.999999. For money, round to two decimal places using a clear rule (half-up is common in retail) and keep intermediate totals at higher precision when you can.
In SQL you often cast integers before dividing, because integer division can truncate. Multiply by 100.0 or cast to decimal types so 1/2 becomes 0.5, not 0.
Unit tests for money helpers should cover 0%, 100%, and awkward values such as 12.5% and recurring fractions. Snapshot expected pennies as integers when you can.
JavaScript has the same floating-point quirks as many languages: 0.1 + 0.2 is not exactly 0.3. For currency, work in integer minor units (pence) where you can, then format for display.
When a figure feeds a decision—payroll, invoices, tax—recompute with a second method or a calculator. A one-minute check is cheaper than reversing a wrong invoice.
If you work with UK take-home pay or duty calculators elsewhere on this site, you will see the same percent factors underneath more complex rules. Mastering the basics here makes those tools less mysterious.
When communicating to non-specialists, pair the percent with absolute numbers: "up 50% from 2 to 3" sets a clearer expectation than "up 50%" alone.
Finally, be kind in communication: round sensibly for humans ("about 1 in 5") while keeping exact figures in the appendix or spreadsheet.
Double-counting is subtle: applying a discount to a VAT-inclusive price when the discount policy applies to net only will disagree with finance. Align with the contract wording before you code the cart.
Multiply the number by the percent and divide by 100. Example: 20% of 80 is 80 × 20 ÷ 100 = 16.
Subtract the old value from the new value, divide by the old value, then multiply by 100.
Divide the final amount by (1 + percent/100). Example: 120 after a 20% increase comes from 120 ÷ 1.2 = 100.
Multiply the net price by 1.20. A £100 net item becomes £120 gross.
Divide the gross price by 1.20. You can also take the VAT portion as gross ÷ 6 when VAT is 20%.
No. Two 10% reductions multiply: ×0.9 ×0.9 = ×0.81, which is 19% off in total.
Percentage points measure the arithmetic gap between two rates. Percent change measures relative change against the starting rate.
Use the free percentage calculator on mfaysal.com for of/change problems, plus the discount and VAT calculators for shop and invoice maths.
Last checked: 18 October 2026. Specs and docs can change, so confirm anything important with the official source linked above.
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