Math

Percentage Calculator

Work with percentages the way people ask them: find a percent of a number, reverse a percent, compare two values, or apply an increase or decrease.

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What is % of ?

Updates as you type

Result

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The formula

Pick a question from “I want to…”, enter the numbers, and read the answer in the result panel. Under the hood every mode uses the same relationship: P% × V₁ = V₂ — or a small variation for difference and change. Percentage difference divides by the average of both values; percentage change divides by the starting value only.

P% × V₁ = V₂ · Difference = |V₁ − V₂| ÷ average × 100 · Change = (New − Old) ÷ |Old| × 100

Worked example

  1. Choose “What is X% of Y?” and enter 15 and 200.
  2. Convert the percent: 15% = 15 ÷ 100 = 0.15.
  3. Multiply: 0.15 × 200 = 30.

Result: 30 (15% of 200)

How percentage problems are solved

Percent means “per hundred.” Most everyday questions rearrange one equation; difference and change use different denominators on purpose.

The core identity

P% × V₁ = V₂ connects a percentage P, a base V₁, and a part V₂. Solving for any missing variable is algebra on that identity (or “is / of × 100” in phrase form).

Difference vs change

Percentage difference asks how far apart two values are relative to their average — useful when neither is a natural start. Percentage change asks how much a value moved relative to its start (or applies a signed percent to a number).

Compounding percents

Successive percent changes multiply growth factors. A 10% rise then a 10% fall yields 0.9 × 1.1 = 0.99 of the original — not a round trip to 100%.

Interesting facts

From Latin

“Percent” comes from per centum — “by the hundred.” A percent is simply a fraction with denominator 100.

Difference ≠ change

Percentage difference divides by the average of both values. Percentage change divides by the starting value only.

Basis points

Finance often quotes rate moves in basis points: 1 bp = 0.01 percentage points. A cut from 5.00% to 4.75% is 25 bp.

Of what?

“20% more” needs a base. 20% more than 50 is 60; 20% of 50 is 10. Ambiguous headlines skip the base.

Successive percents

A 10% rise then a 10% fall does not return to the start: 100 → 110 → 99. Order and compounding matter.

Frequently asked questions

Choose “% change from A to B”, enter the start and end values, then calculate. Or choose “Increase / decrease by %” to apply a percent to a number.

It measures how far apart two numbers are relative to their average — useful when neither value is a clear starting point. Pick “Percentage difference between two values” in the menu.

Yes. Choose “Solve P% × V₁ = V₂”, fill in any two fields, leave one blank, and calculate.

One basis point is 0.01 percentage points. A rate move from 5.00% to 4.75% is a 25 bp cut — common language in finance.

Percents compound on the current base. 100 → 110 (+10%), then 110 × 0.9 = 99 (−10%).

References

  1. Percent — math glossary — National Institute of Standards and Technology (NIST) / SI education context SI literacy context; percent is a pure ratio scaled by 100.
  2. Consumer math — percentages — U.S. Securities and Exchange Commission (Investor.gov) Helpful when percents appear in finance disclosures.