📊 Percentages, Rates & Data Analysis

Percentage & Statistics Calculators

Fast, error-free solvers for percentage calculations, percentage increases, statistical distributions, variance, and probability. Instant client-side computation with complete step-by-step math proofs.

⚡ Quick 3-Way Percentage Calculator

What is P% of X?
What is % of
Result: 37.5
X is what % of Y?
is what % of
Result: 25.00%
Percent Change from A to B
From to
Result: +50.00% (Increase)

Explore Percentage & Statistics Calculators

%
Percentage Calculator
Calculate percentages, increases, decreases, fractions to percentage, and tax adjustments.
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Percent Change Calculator
Determine directional relative change between two values with percentage growth or reduction.
Δ%
Percent Difference Calculator
Calculate symmetric absolute percentage difference between two experimental values.
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Reverse Percentage Calculator
Find original pre-tax or pre-discount quantities from final numbers and percentage rates.
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Mean, Median & Mode Calculator
Find central tendency, middle values, most frequent numbers, and range from any data series.
σ
Standard Deviation Calculator
Calculate sample standard deviation (s), population variance (σ²), sum of squares, and mean.
➕
Average Calculator
Compute arithmetic mean, geometric mean, and weighted average score distributions.
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Probability Calculator
Solve single event, independent union (A ∪ B), conditional P(A|B), and combinatoric odds.
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Tip Calculator
Split restaurant bills and calculate gratuity percentages across dining parties.
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Discount Calculator
Compute final promotional prices, savings margins, and multi-tier discounts.

Formulas: Percent Change vs. Percent Difference

A common point of confusion in applied mathematics is knowing when to use Percent Change versus Percent Difference:

Percent Change (Directional Growth / Loss)

Used when there is an old (initial) value and a new (final) value over time:

Percent Change = ((VFinal - VInitial) / |VInitial|) × 100%

Percent Difference (Symmetric Comparison)

Used when comparing two parallel quantities where neither came first (e.g. comparing two measurement tools):

Percent Difference = (|V1 - V2| / ((V1 + V2) / 2)) × 100%

Frequently Asked Questions (Percentages)

The word percent stems from the Latin per centum, meaning "by the hundred." Therefore, 15% simply means 15 per 100, or the fraction 15/100 = 0.15.

Yes! If an investment grows from $100 to $300, it gained $200. The percentage increase is ($200 / $100) × 100 = 200% increase. There is no mathematical ceiling on percentage increases.

If you start with $100 and lose 50%, you now have $50. To reach $100 again, you must gain $50 on your new base of $50, which is ($50 / $50) × 100 = 100% gain.