Percentage Calculators

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A percentage expresses a number as a fraction of 100 — the word means 'per hundred' (Latin: per centum). Percentages are used universally to communicate proportions, changes, and rates in a way that is intuitive and comparable across different scales. Whether you're calculating percent yield in chemistry, percent composition in biology, percent change in a measurement, or concentration in a solution, the underlying formula is the same: divide part by whole and multiply by 100.

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The Percentage Formula

Percentage = (Part / Whole) × 100

Example: 45 out of 180 samples positive → (45/180) × 100 = 25%

Core Percentage Calculations

Finding a Percentage of a Number

X% of Y = (X/100) × Y
35% of 240 = 0.35 × 240 = 84

What Percentage Is A of B?

% = (A/B) × 100
18 is what % of 72? → (18/72) × 100 = 25%

Percent Change

% change = ((New − Old) / Old) × 100
Value rises 80 → 104: ((104−80)/80) × 100 = 30%

Reverse Percentage (Finding the Original Value)

Original = Final / (1 + % increase/100)
After 20% increase the price is $60 → Original = 60/1.20 = $50

Percentages in Science

  • Percent yield: (Actual yield / Theoretical yield) × 100
  • Percent error: |Measured − True| / True × 100
  • Percent composition: Mass of element / Molar mass × 100
  • GC content: (G + C bases) / Total bases × 100
  • Solution concentration (% w/v, % v/v, % w/w): Mass or volume per 100 mL or 100 g

Converting Between Forms

  • Fraction → Percent: divide and multiply by 100 (3/4 = 75%)
  • Decimal → Percent: multiply by 100 (0.375 = 37.5%)
  • Percent → Decimal: divide by 100 (62% = 0.62)

Glossary

Percentage
A number expressed as a fraction of 100: (Part/Whole) × 100. Used to express proportions, concentrations, error, yield, and change in a standardized, scale-independent way.
Percent Change
((New − Old)/Old) × 100. Measures relative change from an original value. Positive = increase; negative = decrease. Divide by the original (old) value, not the new one.
Percent Yield
(Actual yield / Theoretical yield) × 100%. Expresses how much of the maximum possible product was obtained experimentally. Values below 100% reflect incomplete reaction, side reactions, or purification losses.

Frequently Asked Questions

Percentage = (Part / Whole) × 100. For example, 30 out of 120 = (30/120) × 100 = 25%. To find X% of a number Y: (X/100) × Y. To find what percent A is of B: (A/B) × 100. These three variants cover most percentage problems encountered in science and everyday calculations.

% change = ((New − Old) / Old) × 100. Positive = increase; negative = decrease. Example: a measurement increases from 50 to 65: ((65−50)/50) × 100 = 30% increase. Example: drops from 200 to 150: ((150−200)/200) × 100 = −25%, a 25% decrease. Always divide by the original (old) value, not the new one.

Percent yield = (Actual yield / Theoretical yield) × 100%. Theoretical yield is the maximum product predicted by stoichiometry; actual yield is what you obtained experimentally. Example: reaction should produce 8.5 g but you obtained 7.2 g → % yield = (7.2/8.5) × 100 = 84.7%. Values below 100% reflect losses from incomplete reaction, side reactions, or purification steps.

Original = Final / (1 + %/100). For example, after a 25% increase the value is 75: Original = 75/1.25 = 60. For a percent decrease: Original = Final / (1 − %/100). After a 10% decrease the value is 90: Original = 90/0.90 = 100. Note that a 20% increase followed by a 20% decrease does NOT return to the original — it gives 96% of the original.