Percent Calculators

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Percent (%) means 'per hundred' — it expresses a quantity as a fraction of 100. Percent calculations are among the most common mathematical operations in everyday life, science, and business. Key operations include finding what percent one number is of another (part/whole × 100), calculating a percentage of a number (number × percent/100), finding percent change (new−old)/old × 100, and converting between percentages, fractions, and decimals. Percentages are used for concentrations, error rates, yields, statistics, financial returns, and countless scientific applications.

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Core Percent Formulas

What percent is A of B? = (A/B) × 100

What is X% of N? = N × X/100

Percent change: = (new − old)/old × 100

Find the whole from percent: Whole = Part / (Percent/100)

Worked Examples

  • What percent is 35 of 140? (35/140) × 100 = 25%
  • What is 15% of 80? 80 × 0.15 = 12
  • A drug reduces pain by 40%; original score 70: new score = 70 × (1 − 0.40) = 42
  • A population of 500 increased to 650: % change = (650−500)/500 × 100 = +30%

Percent Conversions

Percent → decimal: divide by 100 (25% = 0.25). Decimal → percent: multiply by 100 (0.73 = 73%). Percent → fraction: write as denominator 100, simplify (40% = 40/100 = 2/5). Fraction → percent: divide numerator by denominator × 100 (3/8 = 0.375 = 37.5%).

Scientific Percent Calculations

  • Percent yield: (actual yield/theoretical yield) × 100
  • Percent error: |measured − true|/true × 100
  • Percent composition: mass of element/total molar mass × 100
  • Percent transmittance: %T = (I/I₀) × 100; OD = 2 − log(%T)

Glossary

Percent (%)
'Per hundred'; expresses a quantity as a fraction of 100; percent = (part/whole) × 100; used for concentrations, changes, yields, errors, and countless scientific calculations.
Percent Yield
(Actual yield / theoretical yield) × 100; measures reaction efficiency; below 100% due to incomplete reactions, side reactions, and product losses during purification.
Percent Error
|Measured − True| / True × 100; quantifies measurement accuracy relative to a known true value; used in analytical chemistry and physics laboratory calibration.

Frequently Asked Questions

Percent means 'per hundred' — it expresses one quantity as a fraction of another, multiplied by 100. Core formula: percent = (part/whole) × 100. To find what percent 45 is of 180: (45/180) × 100 = 25%. To find X% of a number: number × X/100. To find 30% of 240: 240 × 0.30 = 72. To find the whole when you know part and percent: whole = part / (percent/100). Example: 25 is 20% of what number? whole = 25/0.20 = 125.

Percent change = (new value − old value) / old value × 100. Positive result = increase; negative result = decrease. Examples: price rises from $40 to $52: change = (52−40)/40 × 100 = +30%. Population falls from 800 to 640: change = (640−800)/800 × 100 = −20%. Note: percent change from A to B is not the same as from B to A — a 50% increase followed by a 50% decrease returns to 75% of the original (not 100%), because the denominator changes.

Percent to decimal: divide by 100 (75% = 0.75; 0.5% = 0.005). Decimal to percent: multiply by 100 (0.45 = 45%; 1.2 = 120%). Percent to fraction: write as /100 and simplify (60% = 60/100 = 3/5). Fraction to percent: divide numerator by denominator then × 100 (7/8 = 0.875 = 87.5%). For repeating fractions: 1/3 = 0.333... = 33.3%; 2/3 = 66.7%.

Percent yield = (actual yield / theoretical yield) × 100. Theoretical yield is the maximum product calculated from the limiting reagent using stoichiometry. Actual yield is what you actually collect in the experiment. Example: synthesis reaction should produce 15.0 g of product (theoretical) but you collect 11.7 g: % yield = (11.7/15.0) × 100 = 78%. Yield below 100% occurs due to: incomplete reactions, side reactions, product loss during purification, and transfer losses. Yields > 100% indicate incomplete drying, impurities in product, or calculation errors.