Math Calculators

Formula: ((New – Old) / Old) × 100. Example: from 80 to 100 is ((100 – 80) / 80) × 100 = 25% increase. Use the Percentage Change Calculator for instant results with both increase and decrease.

Divide both numerator and denominator by their GCF. Example: 12/18 — GCF is 6, so 12/6 = 2 and 18/6 = 3, giving 2/3. Use the Fraction Calculator which automatically simplifies all results.

Non-perfect squares have irrational square roots. √2 = 1.41421356, √3 = 1.73205080, √5 = 2.23606797 — these decimals go on forever without repeating. Use the Square Root Calculator for any number, including cube roots and nth roots.

Area = π × radius². For radius 5: Area = 3.14159 × 25 = 78.54 square units. From diameter: Area = π × (diameter / 2)². Use the Area Calculator for circles, squares, rectangles and triangles.

In any right triangle: a² + b² = c², where c is the hypotenuse. To find hypotenuse: c = √(a² + b²). Legs of 3 and 4 give hypotenuse = √25 = 5. Use the Pythagorean Theorem Calculator to find any missing side.

I=1, V=5, X=10, L=50, C=100, D=500, M=1000. Subtract when a smaller numeral precedes a larger one: XIV = 10 + (5–1) = 14. MCMXCIX = 1000 + 900 + 90 + 9 = 1999. Use the Roman Numeral Converter for instant two-way conversion.

Steps: find the mean, subtract mean from each value and square it, average those squared differences (= variance), take the square root. Use population SD when you have all data; sample SD (divides by n–1) for a subset. Use the Standard Deviation Calculator for any dataset.

The GCF is the largest number dividing evenly into two or more numbers. For 24 and 36: factors of 24 are 1,2,3,4,6,8,12,24; factors of 36 are 1,2,3,4,6,9,12,18,36; GCF = 12. Use the GCF Calculator for any set of numbers instantly.

Slope = rise / run = (y2 – y1) / (x2 – x1). For points (2, 3) and (6, 11): slope = (11 – 3) / (6 – 2) = 2. Positive slope goes up, negative goes down, zero is horizontal, undefined is vertical. Use the Slope Calculator with any two coordinate points.

Probability = favorable outcomes / total possible outcomes. Rolling a 3 on a six-sided die: 1/6 = 16.67%. Ranges from 0 (impossible) to 1 (certain). For independent events, multiply individual probabilities. Use the Probability Calculator for single and combined events.