
Perimeter Formulas: All Shapes with Variables and Worked Examples
The perimeter of a 2D shape is the total length of its boundary — found by adding the lengths of all its sides. Common shortcuts include P = 4a (square), P = 2(l + w) (rectangle), and C = 2πr (circle).
Apr 26, 2026#Math Formula

Triangle Formula: Area, Perimeter, and All Types Explained
The most common triangle formulas are A = ½ × base × height for area and P = a + b + c for perimeter. Other formulas - Heron's formula, the trigonometric area formula, and per-type formulas for equilateral, isosceles, and right triangles - apply depending on what information you have. The decision table further down shows which formula to use in which case.
Apr 26, 2026#Math Formula

Geometric Sequence Formulas: nth Term, Sum, and Examples
The geometric sequence formulas cover three things: the nth term aₙ = a · r^(n−1), the sum of the first n terms Sₙ = a(1 − rⁿ)/(1 − r) for r ≠ 1, and the infinite sum S∞ = a/(1 − r) when |r| < 1. The first formula finds any single term; the other two add up multiple terms.
Apr 26, 2026#Math Formula

Arithmetic Sequence Formula: nth Term, Sum & Common Difference
The arithmetic sequence formula has two parts: aₙ = a₁ + (n−1)d for the nth term and Sₙ = (n/2) × [2a₁ + (n−1)d] for the sum of n terms. Here a₁ is the first term, d is the common difference, and n is the position. Use (n−1) - not n - when counting the jumps between terms.
Apr 26, 2026#Math Formula

Double Angle Formulas: Sin, Cos, Tan Identities
The double angle formulas are sin 2θ = 2 sin θ cos θ, cos 2θ = cos²θ − sin²θ (also 1 − 2 sin²θ and 2 cos²θ − 1), and tan 2θ = 2 tan θ / (1 − tan²θ). All three are derived from the sum formulas by setting α = β = θ. The cosine has three equivalent forms because the Pythagorean identity converts between them.
Apr 26, 2026#Math Formula

20 Best Online Math Classes for Kids in 2026 (Ranked)
The best online math class depends on what you're solving for - a foundation gap, grade-level practice, enrichment, or budget. Bhanzu leads for structured foundation rebuilding in K–10, and Khan Academy as the free baseline every family should have.
Apr 26, 2026#Math

Volume Formulas for All 3D Shapes
Volume measures the space a 3D shape occupies, expressed in cubic units (cm³, m³, in³). Each shape has its own formula - cube uses V = a³, cuboid uses l × b × h, cylinder uses πr²h, sphere uses ⁴⁄₃ πr³, and cones and pyramids hold exactly one-third of their corresponding cylinder or prism.
Apr 25, 2026#Math Formula

Slope Formula: How to Find the Slope of a Line
The slope formula is m = (y₂ − y₁) / (x₂ − x₁) - it calculates the steepness and direction of a line from any two points on it. Slope can be positive (line rises), negative (line falls), zero (horizontal), or undefined (vertical). The formula is also written as rise over run, where rise = Δy and run = Δx.
Apr 25, 2026#Math Formula

Distance Formula in Maths: Definition, Derivation, and Examples
The distance formula, d = √[(x₂ − x₁)² + (y₂ − y₁)²], gives the straight-line distance between two points on a coordinate plane. It is derived from the Pythagorean theorem and extends to 3D by adding a z-coordinate term.
Apr 25, 2026#Math Formula

Geometry Formulas: Area, Perimeter & Volume for 2D and 3D Shapes
Geometry formulas calculate the perimeter and area of 2D shapes (square, rectangle, triangle, circle) and the surface area and volume of 3D shapes (cube, cuboid, cylinder, cone, sphere). Perimeter uses linear units (cm), area and surface area use square units (cm²), and volume uses cubic units (cm³).
Apr 25, 2026#Math Formula

Integration Formulas: Complete List with Examples
Integration formulas are the standard antiderivative results used to solve integrals across Class 11, 12, and JEE - covering basic, trigonometric, inverse trigonometric, exponential, logarithmic, hyperbolic, and special integrals. The general form is ∫f'(x) dx = f(x) + C.
Apr 25, 2026#Math Formula
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