Percentage Calculator

How Percentages Work

A percentage is simply a number expressed as a fraction of 100. The word “percent” literally means “per hundred.” When you see 25%, it means 25 out of every 100, or 0.25 as a decimal, or 1/4 as a fraction.

This calculator handles four common percentage operations: finding X% of a number, finding what percentage one number is of another, calculating percentage change (increase or decrease), and calculating percentage difference between two values.

Key takeaway: Every percentage problem boils down to one of these four operations. Identify which one you need, and the math is straightforward.

The Four Calculation Modes

What is X% of Y? — Multiply the number by the percentage as a decimal. Example: 18% of $85 = $85 × 0.18 = $15.30. Use this for tips, discounts, tax calculations, and proportions.

X is what % of Y? — Divide the part by the whole and multiply by 100. Example: 42 out of 50 = (42 ÷ 50) × 100 = 84%. Use this for test scores, budget proportions, and performance metrics.

Percentage change — Measures how much a value increased or decreased relative to its original value: ((New - Old) ÷ Old) × 100. Example: salary from $52,000 to $58,500 = +12.5%. Note that percentage changes are asymmetric — a 50% increase followed by a 50% decrease doesn’t return to the original value.

Percentage difference — Measures how far apart two values are relative to their average: |A - B| ÷ ((A + B) ÷ 2) × 100. Unlike percentage change, this has no direction and treats both values equally. Use it to compare two independent measurements, prices, or scores.

Tip: Not sure whether to use percentage change or percentage difference? If you have a clear “before” and “after,” use percentage change. If you’re comparing two independent values with no time relationship, use percentage difference.

Mental Shortcuts

Quick percentage tricks for everyday use:

Example: To calculate an 18% tip on $85, start with 10% ($8.50), add another 10% ($8.50), then subtract 2% ($1.70). That gives you $8.50 + $8.50 – $1.70 = $15.30.

Common Percentage Pitfalls

Percentages don’t add up symmetrically. A 20% increase followed by a 20% decrease doesn’t return to the starting value. $100 + 20% = $120. $120 - 20% = $96. You’re down $4.

The base matters. A $15 increase on a $50 item is 30%. The same $15 increase on a $500 item is 3%. Always consider what the percentage is relative to.

Key takeaway: When you see a percentage in a headline or ad, always ask “percent of what?” A “50% off” sale and a “buy one get one free” deal are mathematically identical — but the framing changes how people perceive the value.