Percentage Calculator

How to Use the Percentage Calculator

Choose one of six modes, enter the values for that mode, and press Calculate to see the result and formula.

1. Select a mode: percent of a number, what percent, percent increase, percent decrease, percent difference, or find original value.
2. Enter the numbers required for the selected mode (decimals allowed).
3. Press Calculate.
4. Review the result and the formula shown for that mode.
5. Switch modes or press Reset to try another scenario.

Methodology & percentage formulas

Percentage calculations evaluate relative ratios out of 100 parts. The calculator evaluates six distinct mathematical relationship modes: Proportion (X% of Y = (X ÷ 100) × Y), Ratio Share ((X ÷ Y) × 100), Percentage Increase (((New − Old) ÷ Old) × 100), Percentage Decrease (((Old − New) ÷ Old) × 100), Symmetric Difference (|X − Y| ÷ ((X + Y) ÷ 2) × 100), and Base Value Reversal (X ÷ (Y ÷ 100)).

Calculations strictly guard against mathematical singularities such as division by zero (e.g. attempting percentage increase from an initial base of zero).

Worked examples

• Percentage of a number: (X / 100) × Y. Example: 20% of 150 = 30.
• What percentage: (X / Y) × 100. Example: 30 is 20% of 150.
• Percentage increase: ((Y − X) / X) × 100. Example: 100 → 125 = 25% increase.
• Percentage decrease: ((X − Y) / X) × 100. Example: 125 → 100 = 20% decrease.
• Percentage difference: |X − Y| / ((X + Y) / 2) × 100. Symmetric comparison — not the same as change from a fixed baseline.
• Find the original value: X / (Y / 100). Example: 30 is 20% of 150.

When to use each mode

• X% of Y: tips, tax estimates, exam scores, data analysis.
• What % is X of Y: comparing a part to a whole.
• Increase / decrease: price changes, growth, or shrinkage from a known starting point.
• Percentage difference: comparing two measurements when neither is clearly the baseline.
• Find original: reverse percentage problems (e.g. “30 is 20% of what?”).

Common mistakes

• Using percentage difference when you meant increase/decrease from a starting value.
• Dividing by zero (zero start for change modes, or zero average for difference).
• Using this tool for retail sale pricing — use Discount Calculator for sale price and savings.

Limitations

General percentage math only. For sale prices use Discount Calculator. Some modes reject divide-by-zero cases (e.g. zero base).

FAQ

How do I calculate a percentage?

Choose the mode that matches your question. For “what is X% of Y”, use Percentage of a Number. For “X is what % of Y”, use What Percentage. Each mode shows the formula used.

How do I find X% of a number?

Select Percentage of a Number, enter the percentage and the number, then Calculate. Formula: (X / 100) × Y. Example: 20% of 150 = 30.

How do I calculate percentage increase?

Select Percentage Increase, enter the starting value and the new value. Formula: ((new − start) / start) × 100. Example: 100 to 125 = 25% increase.

How do I calculate percentage decrease?

Select Percentage Decrease, enter the starting value and the new value. Formula: ((start − new) / start) × 100. Example: 125 to 100 = 20% decrease.

What is the difference between percentage difference and percentage change?

Percentage increase/decrease measures change from a starting value. Percentage difference compares two values symmetrically: |X − Y| / average × 100. Use difference when neither value is clearly the baseline.

How do I find the original number when I know a part and a percent?

Select Find the Original Value. Enter the part value and the percentage. Formula: part / (percent / 100). Example: 30 is 20% of 150.

Can I use decimal percentages?

Yes. Enter decimal percentages and decimal numbers (e.g. 12.5% of 80). Results support decimal output.

Can I use negative numbers?

Some modes accept negative values where the math is defined. Increase, decrease, and difference reject a zero starting value or zero average where the formula would divide by zero.

How does the calculator round results?

Intermediate calculations use full precision. Displayed results are rounded for readability (typically up to four decimal places for most values, with trailing zeros trimmed).

What is the difference between Percentage Calculator and Discount Calculator?

Percentage Calculator covers general percentage math (percent of, reverse percent, change, difference). Discount Calculator focuses on sale price, discount amount, savings, and optional tax on a product price.