What the Percentage Calculator Does

This percentage calculator handles the three questions people ask most often about percentages, all in one place. You can find the percent of a number, work out what percentage one number is of another, and measure the percent change between two values.

It is useful for anyone working with discounts, tips, tax, grades, commissions, interest, or data comparisons. Students checking homework, shoppers verifying a sale price, and analysts measuring growth can all get an exact answer without doing the arithmetic by hand.

How It Works: The Three Percentage Formulas

Each mode uses a simple, standard formula. "Percent" literally means "per hundred," so every calculation involves dividing or multiplying by 100.

Pick the mode that matches your question, plug in your two known values, and the calculator applies the matching formula below.

Percent of a number: X% of Y = (X / 100) × Y
X is what percent of Y: percentage = (X / Y) × 100
Percent change: change = ((new − old) / |old|) × 100

Worked Examples With Real Numbers

Percent of a number: To find 15% of 80, compute (15 / 100) × 80 = 0.15 × 80 = 12. So 15% of 80 is 12.

X is what percent of Y: To find what percent 45 is of 180, compute (45 / 180) × 100 = 0.25 × 100 = 25. So 45 is 25% of 180.

Percent change: A price rises from 50 to 65. The change is ((65 − 50) / 50) × 100 = (15 / 50) × 100 = 30. That is a 30% increase. If the price instead fell from 65 to 50, the result is ((50 − 65) / 65) × 100 ≈ −23.08%, a decrease of about 23.08%.

Percent Change vs. Percentage Points

A common mistake is confusing percent change with percentage points. If an interest rate goes from 4% to 6%, that is a rise of 2 percentage points, but a percent change of ((6 − 4) / 4) × 100 = 50%.

Use percentage points when comparing two percentages directly. Use percent change when measuring how much a value grew or shrank relative to its starting point.

Tips and Common Mistakes

Small errors usually come from mixing up which number is the base or applying percentages in the wrong order. Keep these points in mind:

Identify the base (the "of" number) first. In "what percent is X of Y," Y is the base and goes in the denominator.
A 50% increase followed by a 50% decrease does not return to the original. Starting at 100: 100 → 150 → 75.
Percentage decreases can never exceed 100%, but increases can (doubling a value is a 100% increase).
For percent change, the denominator is always the old value, not the new one.
To reverse a discount, do not just add the percent back. A 20% discount means you paid 80%, so the original price is the sale price divided by 0.80.

Factors That Affect Your Result

The biggest factor is which value you treat as the reference point, since the same two numbers can produce different percentages depending on the base. Rounding also matters: rounding intermediate steps can shift the final answer, so round only at the end.

Finally, watch the sign in percent change. A negative result means a decrease and a positive result means an increase, which is easy to overlook when comparing several figures at once.