Percentage Calculator

Every mode is a rearrangement of the same relationship between a part, a whole, and a percentage, solved for whichever piece is unknown:

• What is P% of Y? — multiply: Y × (P ÷ 100). 20% of 80 = 16.
• X is what percent of Y? — divide then scale: (X ÷ Y) × 100. 20 of 80 = 25%.
• X is P% of what number? — divide by the decimal: X ÷ (P ÷ 100). 20 is 25% of 80.
• Percentage change (old → new) — ((New − Old) ÷ |Old|) × 100, labelled increase, decrease, or no change.
• Increase / decrease by a percent — Base ± (Base × P ÷ 100).
• Decimal ↔ percent — a percent is a decimal × 100 (0.25 = 25%).
• Fraction → decimal & percent — numerator ÷ denominator, × 100 (1/4 = 0.25 = 25%).

Percent-of and percent-change are not the same calculation. "What percent is 20 of 80" (25%) measures a part against a whole at one moment; "80 → 100" (a 25% increase) measures how much a value moved from a starting point. Feeding the wrong one into a decision is a common and costly mistake — the modes are kept separate here for exactly that reason.

Percentage vs percentage points. If a rate rises from 3% to 5%, that is a 2 percentage-point rise but a 66.7% percent change relative to the original 3%. The change mode reports the percent change; the arithmetic difference of 2 points is a separate idea.

Example 1 — a test score. A student scored 47 out of 50. (47 ÷ 50) × 100 = 94%.

Example 2 — a share of a budget. Rent is $1,350 of a $4,500 monthly budget. (1,350 ÷ 4,500) × 100 = 30% of the budget goes to rent.

Example 3 — part larger than whole. This quarter's sales were $120,000 against last quarter's $80,000. (120,000 ÷ 80,000) × 100 = 150% — this quarter is 150% of last quarter (half again as large).

The result tells you how big the part is relative to the whole, on a scale where the whole equals 100%. A result of 50% means the part is exactly half the whole; 100% means they are equal; above 100% means the part exceeds the whole. Because the answer is always relative to the whole you chose, make sure the whole is the true total you mean to compare against — changing the whole changes the percentage even when the part stays the same.

A quick reference for common part-of-whole percentages:

• 1 of 3 ≈ 33.3%; 2 of 3 ≈ 66.7%
• 1 of 4 = 25%; 3 of 4 = 75%
• 1 of 8 = 12.5%; 1 of 6 ≈ 16.7%
• 1 of 20 = 5%; 1 of 50 = 2%; 1 of 200 = 0.5%

Reach for this calculator for almost any everyday percentage question: taking a percent of a number (tips, commissions, allocations), expressing one quantity as a share of another (test scores, budget shares, progress), working backwards from a percentage to the original whole, measuring how much a value grew or shrank between two points, nudging a number up or down by a percent, or converting between fractions, decimals, and percents. Switch modes with the selector at the top of the tool, or tap a preset to load a worked example.

• Division by zero is undefined. A whole of zero (“what percent of 0”), a percentage of zero in the reverse mode, an original value of zero in change mode, and a fraction denominator of zero all produce a clear error instead of a number.
• Negative numbers are allowed and handled literally — percentage change uses the absolute value of the original so the sign reflects direction — but read negative-base results carefully; they are easy to misinterpret.
• Rounding: results are shown to at most six decimal places. For long chained calculations, keep the full-precision figure rather than re-typing a rounded one.
• For adding or removing sales tax or a store discount specifically, the Sales Tax and Discount calculators frame the same math around price and savings.