Mathematics formulas
Algebra, geometry, trigonometry, calculus, and statistics formulas.
Pythagorean Theorem
a² + b² = c²
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Finds the solutions (roots) of any quadratic equation ax² + bx + c = 0. The discriminant b² - 4ac determines the number of real solutions.
Area of a Circle
A = πr²
Calculates the area enclosed by a circle given its radius.
Circumference of a Circle
C = 2πr
Calculates the perimeter (distance around) of a circle.
Distance Formula
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Finds the straight-line distance between two points in a 2D plane. Derived directly from the Pythagorean theorem.
Slope Formula
m = (y₂ - y₁) / (x₂ - x₁)
Measures the steepness of a line — how much y changes per unit change in x.
Area of a Triangle
A = ½ × base × height
Calculates the area of a triangle using base and height. The height must be perpendicular to the chosen base.
Law of Cosines
c² = a² + b² - 2ab·cos(C)
Generalizes the Pythagorean theorem to any triangle. When C = 90°, cos(C) = 0 and it reduces to a² + b² = c².
Standard Deviation Formula
σ = √(Σ(xi - μ)² / N)
Measures how spread out data points are from the mean. A low SD means data is clustered close to the mean; a high SD means data is spread out.
Permutations Formula
P(n,r) = n! / (n-r)!
Counts the number of ways to arrange r items from a set of n, where ORDER MATTERS.
Combinations Formula
C(n,r) = n! / (r!(n-r)!)
Counts the number of ways to choose r items from n, where ORDER DOES NOT MATTER.