Math calculator

Percentage Calculator

Q: What is a percentage?

A number or ratio expressed as a fraction of 100, usually written with %. Example: 25 out of 100 is 25%.

Q: How do you calculate a percentage?

Divide the part by the whole, then multiply by 100: percentage = (part / whole) × 100.

Q: What is P% of X?

Multiply X by P/100. Example: 20% of 250 = 250 × 0.2 = 50.

Q: How do I find what percent X is of Y?

Compute 100 × X / Y. Example: 50 is what % of 200? → 25%.

Q: How do I find the whole when I know the part and percent?

Whole = 100 × part / percent. Example: 12 is 20% of what? → 60.

Q: Percent change vs percent difference?

Change compares a new value to an old starting value using |old| in the denominator. Difference divides |A−B| by the average of two non-negative values A and B — useful when neither value is a natural baseline.

Q: How do I increase or decrease a number by a percent?

New = X × (1 + P/100) to increase, or X × (1 − P/100) to decrease.

Q: Why does percent change use |old|?

So a move from −100 to −50 is a +50% increase (less negative), not a sign flip from the denominator. The dedicated Percentage Change calculator uses the same convention. Percent change is still undefined at old = 0.

Q: Can percentage difference use negative numbers?

No. This page defines percentage difference for A ≥ 0, B ≥ 0, and A+B ≠ 0. A = −10 and B = 10 would make the average 0; two negatives can make the unsigned formula look signed. Use percent change when a signed baseline exists.

Q: Why do percentages matter?

They show discounts, taxes, tips, grades, growth rates, and comparisons in a common 0–100 scale.

Calculate percentages, percentage of a number, and “what percent is X of Y” with clear arithmetic steps. Runs locally in your browser. Try it free.

Calculation error

Percentage

—

Enter value A (API: MISSING_REQUIRED_INPUT).

Inputsmode=diff

Mode—

FormulaY = X × P / 100

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance

Input interpretation: mode=diff
Result: Percentage: —
Assurance: Core
Declared partition coverage: PASS · 9/9 declared partitions (of, is-what, of-what, change, adjust-up, adjust-down, difference, invalid-domain, xcal) · Matrix
Known limitations: SI percent = 0.01; modes of / is-what / of-what / change / adjust-up / adjust-down / difference
Core CVP does not include live graph, viewport, or pointer interaction.
Model: Common percentage phrases: % of, is what %, of what, percent change, ±P% adjust, and percentage difference.
Scope: Interactive evaluation runs locally in the browser. Shared URLs and REST evaluate the same versioned engine (query SSR).
Verification: Engine tested · Source checked · v1.1.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance· View Manifest · CVP overview · Specification
Versions: Calculation 1.1.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-08.xcal
Verification revision: 2026-09-08.xcal · 2/2 property · digest e1b745d88212
Legacy regression: 19/19 tests · Production surface contract 5/5
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review: Not performed
Named expert review: Not performed
CVP suite: 2/2 golden · 7/7 CVP boundary · 7/7 invalid · 2/2 property · 2/2 metamorphic · 2/2 round-trip · 1/1 cross-interface · 3/3 cross-calculator · 1/1 CVP contract · Manifest
Sources: BIPM — The International System of Units (SI), 9th edition — Units accepted for use with the SI — percent (symbol %), 1% = 0.01
NIST Special Publication 811 — Guide for the Use of the International System of Units (SI) — Writing values of quantities — the percent
CalculatorX percentage conventions — Six phrase modes, |old| percent change, non-negative percentage difference
NIST — SI Unit Rules and Style Conventions — Percent and fractions
Sources
Evidence: 12 legacy golden · 7 legacy boundary · legacy regression suite · 2/2 oracle-backed golden · 7/7 invalid · Artifact integrity PASS
Semantic contract: PASS

Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Percent change uses |old| in the denominator — the same signed convention as Percentage Change.

P% of XY = X × P / 100

X is what % of YP = 100 × X / Y

X is P% of whatY = 100 × X / P

Percent changeΔ% = 100 × (new − old) / |old|

Increase / decreaseY = X × (1 ± P/100)

Percent differenceΔ% = 100 × |A − B| / ((A + B) / 2)Domain: A ≥ 0, B ≥ 0, A + B ≠ 0

iPercent means “per hundred.” 35% = 0.35 = 35/100. Percent change uses |old| in the denominator so a negative starting value keeps the increase/decrease direction. Percentage difference is defined for non-negative A and B.

How to use

Choose a phrase or mode

Pick % of, is what %, of what, change, increase/decrease, or difference.

Enter the known numbers

Use the labels that match how you ask the question in words.

Read the result and steps

See the formula filled with your values.

Example calculations

Common configurations with formula and result.

Percent of

20% of 250

250 × 20/100

Is what percent

50 of 200

100 × 50/200

25%

Of what

12 is 20% of ?

100 × 12/20

Percent change

40 → 50

(50−40)/|40|×100%

25%

Increase by %

500 + 10%

500×1.1

550

Quick examples

Common values at a glance.

Question	Result
What is 20% of 250?	50
50 is what % of 200?	25%
12 is 20% of what?	60
Change from 40 to 50?	+25%
500 increased by 10%?	550
500 decreased by 10%?	450
Difference 10 vs 6?	50%

i Percentage difference uses the average of two non-negative values in the denominator; percent change uses |old| as the baseline.

Percentage calculator specification

Version 1.1.1 · Engine tested

Calculation status

Engine tested 19/19 tests · Production surface contract 5/5
Named expert review Not performed
Calculation version 1.1.1

Review policy · Evidence

Definition: A percentage expresses a number as a fraction of 100. This calculator handles the common phrases: what is P% of X; X is what % of Y; X is P% of what; change from A to B; increase or decrease by P%; and percentage difference between two values.
What it calculates: Common percentage phrases: % of, is what %, of what, percent change, ±P% adjust, and percentage difference.
Inputs: % of: percent P and base X
Is what %: part X and whole Y
Of what: part X and percent P
Change: old and new values
± %: value X and percent P (increase or decrease)
Difference: values A and B
Outputs: The missing amount or percent for the selected phrase
Formula: Y=X·P/100; P=100·X/Y; Y=100·X/P; Δ%=100·(new−old)/|old|; diff%=100·|A−B|/((A+B)/2) for A≥0, B≥0, A+B≠0
Assumptions: Interactive evaluation runs locally in the browser. Shared URLs and REST evaluate the same versioned engine (query SSR).
Denominators (whole, old, average of A and B, P) must be nonzero where required.
Percent change uses |old| in the denominator (signed increase/decrease). Typically used with a nonzero baseline; old = 0 is undefined.
Percentage difference is defined for A ≥ 0, B ≥ 0, and A+B ≠ 0.
Units: Inputs in consistent units; results as amounts or %
Boundary conditions: Division by zero → DIVISION_BY_ZERO
Percentage difference with A < 0 or B < 0 → VALUE_MUST_BE_NON_NEGATIVE
Unknown mode → INVALID_MODE
Example: 20% of 250 = 50
Validation cases: 7 published on this page · 19/19 tests · Production surface contract 5/5 · View evidence
20% of 250 → 50
50 is what % of 200 → 25%
12 is 20% of what → 60
40 → 50 change → 25%
old=−100, new=−50 change → +50% (uses |old|)
10 vs 6 difference → 50%
A=−10, B=10 difference → error VALUE_MUST_BE_NON_NEGATIVE
Sources: BIPM — The International System of Units (SI), 9th edition — Units accepted for use with the SI — percent (symbol %), 1% = 0.01 · accessed 2026-08-28
Supports: Defines percent as the number 0.01 (one part in one hundred). The core relation P% of X = X × P/100 follows from that definition.
NIST Special Publication 811 — Guide for the Use of the International System of Units (SI) — Writing values of quantities — the percent · accessed 2026-08-28
Supports: NIST usage of percent as 0.01 with the SI. Does not prescribe percent-change vs percent-difference conventions.
CalculatorX percentage conventions — Six phrase modes, |old| percent change, non-negative percentage difference
Supports: Percent change Δ% = 100×(new−old)/|old| (undefined at old = 0). Percentage difference Δ% = 100×|A−B|/((A+B)/2) on A ≥ 0, B ≥ 0, A+B ≠ 0. Increase/decrease is X×(1±P/100).
NIST — SI Unit Rules and Style Conventions — Percent and fractions
Supports: The symbol % represents the number 0.01. Thus p% = p/100 and a part of p% of base b equals b×p/100; inverse percentage equations are algebraic rearrangements. CalculatorX’s negative-baseline signed-change convention is separately specified, not attributed to NIST. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.
Calculation version: 1.1.1

Background

Interpretation and common distinctions.

What does this percentage calculator compute?

A percentage expresses a number as a fraction of 100. This calculator handles the common phrases: what is P% of X; X is what % of Y; X is P% of what; change from A to B; increase or decrease by P%; and percentage difference between two values.

The published formula or method is Y=X·P/100; P=100·X/Y; Y=100·X/P; Δ%=100·(new−old)/|old|; diff%=100·|A−B|/((A+B)/2) for A≥0, B≥0, A+B≠0. The following references support the stated mathematics or method:

NIST — SI Unit Rules and Style Conventions: The symbol % represents the number 0.01. Thus p% = p/100 and a part of p% of base b equals b×p/100; inverse percentage equations are algebraic rearrangements. CalculatorX’s negative-baseline signed-change convention is separately specified, not attributed to NIST. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.

Which inputs and limits should you check?

Keep the part, base, and percentage distinct; percent means a ratio multiplied by 100. Follow the selected solve direction and zero-base policy.

The worked example uses 20% of 250 with 250 × 20/100. Compare it with the Example calculations and the complete result for the same inputs.

How can you verify and cite this result?

CalculatorX is responsible for this page. The mathematical references above explain the model; implementation checks and their scope are documented separately in the math.percentage v1.1.1 Evidence and capability contract. Read the displayed verification and production state together with the specification's numerical limits.

Use the clean calculator URL to cite the tool. A shared input link identifies a particular calculation. Content updates, numerical verification, and domain reviews have separate dates and scopes.

What is a percentage?

A percentage is a number expressed as a fraction of 100, written with %. It is a dimensionless way to compare a part to a whole (alongside ratios, fractions, and decimals).

Example: 25 of 50 students are male → 25/50 = 0.5 = 50%.

Core formulas

Y = (X · P)/100 P = (100 · X)/Y Y = (100 · X)/P

Algebraically these are the same relation P(decimal) × V₁ = V₂.

Percent change

% change = (new − old)/(|old|) × 100%

The absolute value in the denominator is a CalculatorX convention (shared with the Percentage Change calculator): a move from −100 to −50 is a +50% increase. Percent change is undefined when old = 0. Negative baselines can still be unintuitive in some domains — say so in the result interpretation.

Increase / decrease by P%

X increased by P% = X(1+P/100), X decreased by P% = X(1−P/100)

Percentage difference

% difference = (|A−B|)/((A+B)/2) × 100% (A ≥ 0, B ≥ 0, A+B ≠ 0)

This page does not extend percentage difference to negative values. A = −10, B = 10 would make the average zero; two negatives can make an unsigned relative-difference look signed. Use percent change when a signed starting value is the baseline.

Other calculators in this family: Percent Error Calculator, Percentage Change Calculator, Proportion Calculator, Ratio Calculator . Explore all Percent, Ratio & Proportion.

Frequently asked questions

Key distinctions behind the calculation.

What is a percentage?

A number or ratio expressed as a fraction of 100, usually written with %. Example: 25 out of 100 is 25%.

How do you calculate a percentage?

Divide the part by the whole, then multiply by 100: percentage = (part / whole) × 100.

What is P% of X?

Multiply X by P/100. Example: 20% of 250 = 250 × 0.2 = 50.

How do I find what percent X is of Y?

Compute 100 × X / Y. Example: 50 is what % of 200? → 25%.

How do I find the whole when I know the part and percent?

Whole = 100 × part / percent. Example: 12 is 20% of what? → 60.

Percent change vs percent difference?

Change compares a new value to an old starting value using |old| in the denominator. Difference divides |A−B| by the average of two non-negative values A and B — useful when neither value is a natural baseline.

How do I increase or decrease a number by a percent?

New = X × (1 + P/100) to increase, or X × (1 − P/100) to decrease.

Why does percent change use |old|?

So a move from −100 to −50 is a +50% increase (less negative), not a sign flip from the denominator. The dedicated Percentage Change calculator uses the same convention. Percent change is still undefined at old = 0.

Can percentage difference use negative numbers?

No. This page defines percentage difference for A ≥ 0, B ≥ 0, and A+B ≠ 0. A = −10 and B = 10 would make the average 0; two negatives can make the unsigned formula look signed. Use percent change when a signed baseline exists.

Why do percentages matter?

They show discounts, taxes, tips, grades, growth rates, and comparisons in a common 0–100 scale.

Percentage Calculator

Formulas

How to use

Choose a phrase or mode

Enter the known numbers

Read the result and steps

Example calculations

Percent of

Is what percent

Of what

Percent change

Increase by %

Quick examples

Percentage calculator specification

Background

What does this percentage calculator compute?

Which inputs and limits should you check?

How can you verify and cite this result?

What is a percentage?

Core formulas

Percent change

Increase / decrease by P%

Percentage difference

Related tools

Frequently asked questions