Formulas and calculators

Math formulas

A practical reference for algebra, geometry, trigonometry, probability, and statistics.

Math topics

Solve equations and work with algebraic expressions using clearly explained formulas and conditions.

Use geometric relationships to calculate lengths, areas, angles, and other properties of plane figures and solids.

Calculate volumes, surface areas, and dimensions of common three-dimensional solids.

Calculate terms and sums of arithmetic and geometric sequences, including convergent infinite series.

Measure angles in degrees and radians and use trigonometric relationships in right triangles and on the unit circle.

Describe a data set with measures of centre and spread: mean, median, mode, range, variance and standard deviation.

Formula	Equation	Quantities	Open
Quadratic equation	x = (-b ± √(b² - 4ac)) / 2a	quadratic coefficient, linear coefficient, constant term	Open
Pythagorean theorem	c² = a² + b²	first leg, second leg, hypotenuse	Open
Circle area and circumference	A = πr²; C = 2πr	radius, diameter, circumference, area	Open
Triangle area	A = b × h / 2	area, base, perpendicular height, first side, second side, third side	Open
Rectangle area and perimeter	A = a × b; P = 2(a + b)	area, perimeter, first side, second side	Open
Cube and cuboid volume and surface area	Cuboid: V = abc, S = 2(ab + ac + bc); cube: V = a³, S = 6a²	volume, total surface area, cube edge, cuboid length, cuboid width, cuboid height	Open
Arithmetic sequence	aₙ = a₁ + (n - 1) × r; Sₙ = n × (a₁ + aₙ) / 2	first term, common difference, term index, nth term, sum of the first n terms	Open
Geometric sequence	aₙ = a₁ × qⁿ⁻¹; Sₙ = a₁ × (1 - qⁿ) / (1 - q)	first term, common ratio, term index, nth term, sum of the first n terms, sum of the infinite series	Open
Degrees and radians	α[rad] = α[°] × π / 180	angle, converted angle, normalised angle, whole turns	Open
Mean, median, variance and standard deviation	x̄ = Σxᵢ / n; σ² = Σ(xᵢ − x̄)² / n; s² = Σ(xᵢ − x̄)² / (n − 1)	observations, count, arithmetic mean, median, mode, range, population variance, population standard deviation, sample variance, sample standard deviation	Open