Math calculator

Percentage Calculator

Solve every everyday percentage question in one place: what is X% of Y, what percent one number is of another, the reverse (X is Y% of what), increase or decrease by a percentage, percentage change, percentage difference, discounts with tax, and tax / tip / commission — each with the formula, the steps, and a downloadable Excel workbook.

Transparent assumptions 8 modes in one tool Every formula & step shown Scenario & compare tables 7-sheet Excel workbook Verify figures that matter

Calculate a percentage Percentage formulas

Exact to the precision you choose — verify figures that matter (invoices, tax, payroll).

A percentage is a fraction out of 100, so to take X% of a number you divide X by 100 and multiply. 25% of 200 is 0.25 × 200 = 50 (the other 75% is 150). To go the other way, 50 out of 200 is 50 ÷ 200 × 100 = 25%; and to find the whole, if 50 is 25% of a number that number is 50 ÷ 0.25 = 200.

Common percentage questions

Percent of a number

Percentage

Enter 25 for 25% — supports over 100% and negatives.

Of this number (whole)

The base value (100%).

Results

Result

25% of 200

Remainder (the other 75%)

150

Whole − result.

Decimal equivalent

0.25

25% ÷ 100.

25% of 200 is 50. The remaining 75% is 150. As a decimal, 25% is 0.25.

Formula

Result = (Percentage ÷ 100) × Whole

Convert the percent to a decimal: 25% ÷ 100 = 0.25.
Multiply by the whole: 0.25 × 200 = 50.
Remainder = 200 − 50 = 150.

7 sheets — Quick Solver, common problems, change & difference, shopping/tax/tip, scenario table, formulas, and a 20-question practice sheet.

Visual breakdown

25% of 200

Result (25%) — 50Remainder (75%) — 150

Scenario comparison table

Common percentages of a single base value — the same table is in the workbook’s Scenario sheet, fully editable.

Base value

Custom percentage (optional)

Scenario comparison table
Percentage	Decimal	Result	Remainder	Add %	Subtract %	Use case
1%	0.01	2	198	202	198	1% — a quick scale reference
5%	0.05	10	190	210	190	5% — common small adjustment
10%	0.10	20	180	220	180	10% — move the decimal one place
12%	0.12	24	176	224	176	12% — frequent service charge
15%	0.15	30	170	230	170	15% — standard tip
18%	0.18	36	164	236	164	18% — common GST / higher tip
20%	0.20	40	160	240	160	20% — generous tip or fifth off
25%	0.25	50	150	250	150	25% — one quarter
33.33%	0.333333	66.67	133.33	266.67	133.33	⅓ — one third
37.5%	0.375	75	125	275	125	Your custom percentage
50%	0.50	100	100	300	100	50% — exactly half
75%	0.75	150	50	350	50	75% — three quarters
100%	1.00	200	0	400	0	100% — the whole amount

Compare several rates at once

Enter a base amount and a list of percentages separated by commas — see each one’s amount and total side by side.

Base amount

Percentages (comma-separated)

Compare rates table
Rate	Decimal	Amount	Total (base + rate)
5%	0.05	100	2,100
10%	0.10	200	2,200
15%	0.15	300	2,300
18%	0.18	360	2,360
20%	0.20	400	2,400

Amount = base × rate ÷ 100. Total adds the amount to the base — handy for comparing tip, tax, or fee options.

At a glance

Formula shown: Result = Percentage ÷ 100 × Whole — with reverse, change, and difference variants shown.
Scenario support: Eight modes plus a scenario table and a compare-several-rates tool.
Workbook export: 7-sheet Excel (XLSX) export
Educational estimate: Planning support from the values you enter — not professional advice.

How to read your result

Every mode here reduces to one relationship: Part = Percentage ÷ 100 × Whole — know any two of part, percentage, and whole to find the third, which is exactly what the "find the percentage" and "find the whole" modes solve for. The most commonly confused pair is percentage change and percentage difference: change has a direction and is measured against a starting value, (New − Old) ÷ Old × 100, while difference is symmetric and measures two values against their average, |A − B| ÷ average × 100 — they answer different questions and rarely give the same number for the same pair. Also watch reversed percentages: adding 20% then removing 20% does not return the original, because the second percentage applies to a different (larger) base — to undo an increase you divide by the growth multiplier, not subtract the same percentage again.

Percentage formulas

Percent of a number

Result = Percentage ÷ 100 × Whole

25% of 200 = 0.25 × 200 = 50.

Find the whole (reverse)

Whole = Part ÷ (Percentage ÷ 100)

50 ÷ 0.25 = 200.

Percentage change

Change = (New − Old) ÷ Old × 100

(100 − 80) ÷ 80 × 100 = +25%.

Percentage difference

|A − B| ÷ ((A + B) ÷ 2) × 100

|10 − 6| ÷ 8 × 100 = 50%.

Worked example

25% of 200. 0.25 × 200 = 50. The remaining 75% is 150.

Price changed from 80 to 100. Percentage change = (100 − 80) ÷ 80 × 100 = +25% — a directional measure against the starting value of 80.

Comparing 10 and 6 with no starting point. Percentage difference = |10 − 6| ÷ ((10 + 6) ÷ 2) × 100 = 4 ÷ 8 × 100 = 50% — a different number from a percentage-change calculation on the same pair, because difference measures against the average, not a starting value.

Assumptions

Percentages are entered as whole numbers (25 means 25%, not 0.25); values over 100% and, where valid, negatives are supported.
The “whole” is the 100% base; the part is measured against it.
Percentage change uses the old value as the denominator and is undefined when it is zero.
Percentage difference divides by the average of the two values and is undefined when that average is zero.
In discount mode, tax is applied to the price after the discount; tax you collect is treated as a pass-through, not income.
Results are rounded only for display, to the number of decimals you select; the maths is carried at full precision.

Limitations

This is a math utility: it does not know your local tax rules, rounding conventions, or tipping norms.
It calculates single percentages; it does not compound interest over time or handle multi-step financial schedules.
Percentage change can be misleading when the starting value is negative or crosses zero; interpret such results with care.
Very large numbers may show tiny rounding in the last displayed place.

Need more than a single percentage? For sales tax and VAT/GST see the VAT calculator; for pricing from cost see the markup calculator and profit margin calculator; for before-and-after growth the dedicated percentage change calculator.

Frequently asked questions

How do I calculate what percentage one number is of another?

Divide the part by the whole and multiply by 100: Percentage = (Part ÷ Whole) × 100. For example, 50 out of 200 is 50 ÷ 200 × 100 = 25%. Use the “X is what % of Y” mode, which also shows the decimal and the remaining share.

How do I find X% of a number?

Convert the percentage to a decimal (divide by 100) and multiply by the number: Result = (Percentage ÷ 100) × Whole. 25% of 200 = 0.25 × 200 = 50. The remainder (the other 75%) is 150.

What is the difference between percentage change and percentage difference?

Percentage change measures movement from a starting value and has a direction: (New − Old) ÷ Old × 100 — 80 to 100 is +25%. Percentage difference compares two values with no reference and is symmetric: |A − B| ÷ average × 100 — 10 and 6 differ by 50%. They give different numbers, so they are not interchangeable.

Why does adding 20% and then removing 20% not return the original number?

Because the two percentages are taken from different bases. 100 grown by 20% is 120, but removing 20% takes 20% of 120 (24), leaving 96 — not 100. To undo a 20% increase you divide by 1.20, not subtract 20%. The calculator shows the exact reverse percentage.

Why is percentage change from zero undefined?

Percentage change divides by the old value, and dividing by zero has no answer. Any move away from 0 would also be an “infinite” percentage of nothing. When the starting value is 0, report the absolute change instead, or choose a non-zero reference point — the calculator explains this rather than printing a misleading number.

Read the guide

There is no dedicated guide to general percentage math yet. For the tax/VAT/GST portion of this calculator's tax-and-tip mode, see VAT, GST, and Sales Tax Calculations Explained With Examples.

Educational use disclaimer

This percentage calculator and its Excel workbook are provided for education and everyday estimation. Results are mathematically exact to the precision you select, but they are only as correct as the numbers you enter. The tool does not give financial, tax, accounting, or legal advice and does not know your local tax rules, tipping norms, or rounding conventions. Percentage change is undefined when the starting value is zero, and percentage difference is undefined when the two values average to zero. For decisions that matter — invoices, tax filings, payroll, or contracts — verify the figures with the appropriate professional or official source.

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Authorship & verification

Written and maintained by Jay Sudha

Formula and examples verified on 14 June 2026
Educational estimate only