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Math calculator

Percentage Calculator

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.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance
Input interpretation
Enter values to calculate.
Result
—
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 3/3
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
Sources
Evidence
12 legacy golden · 7 legacy boundary · legacy regression suite · 2/2 oracle-backed golden · 7/7 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.1.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
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

1

Choose a phrase or mode

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

2

Enter the known numbers

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

3

Read the result and steps

See the formula filled with your values.

Example calculations

Common configurations with formula and result.

ϟ

Percent of

20% of 250

250 × 20/100
50
ϟ

Is what percent

50 of 200

100 × 50/200
25%
ϟ

Of what

12 is 20% of ?

100 × 12/20
60
ϟ

Percent change

40 → 50

(50−40)/|40|×100%
25%
ϟ

Increase by %

500 + 10%

500×1.1
550

Quick examples

Common values at a glance.

QuestionResult
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

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 3/3 · 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).
Calculation version
1.1.1

Background

Interpretation and common distinctions.

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, Percentage change, VAT, Fractions .

Δ Percent error › Δ% Percentage change › tax VAT › a/b Fractions ›
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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.