Geometry Calculators

Calculate the area of a circle given its radius (or diameter). A = πr².

A = s² where s is the side length.

A = length × width.

Three formulas: base × height ÷ 2, SAS (two sides and angle), and Heron's (three sides).

A = ½ × (parallel side a + parallel side b) × height.

A = base × height (perpendicular height).

A = (d₁ × d₂) / 2 — half the product of the diagonals.

A = π × a × b, where a and b are the semi-major and semi-minor axes.

A = ½ r² θ (radians) or A = πr² × (θ/360) (degrees).

A = ¼ × n × s² × cot(π/n) for an n-gon with side length s.

P = 2(l + w). Length plus width, doubled.

P = 4s. Four equal sides.

P = a + b + c. Sum of all three sides.

P = a + b + c + d. Sum of two parallel sides + two non-parallel.

C = 2πr (or πd). Area = πr². The fundamental circle formulas.

P ≈ π(a + b)(1 + 3h / (10 + √(4 − 3h))) where h = ((a−b)/(a+b))². Ramanujan approximation.

V = s³. Six equal square faces.

V = l × w × h. Box / cuboid volume.

V = (4/3)πr³. Surface area = 4πr².

V = πr²h. Surface area = 2πr² + 2πrh (top + bottom + side).

V = (1/3)πr²h. One-third of the cylinder of same base and height.

V = (1/3) × base area × height. For square / rectangular / triangular bases.

SA = 6s². Six identical square faces.

SA = 2(lw + lh + wh). Box / cuboid surface.

SA = 4πr². Exactly 4× the area of a great circle of the same radius.

SA = 2πr² + 2πrh. Two circular ends + lateral wrap.

SA = πr² + πrl, where l = √(r² + h²) is the slant height.

Cube: V = s³, SA = 6s², body diagonal = s√3. All three properties from edge length.

Cuboid: V = lwh, SA = 2(lw + lh + wh), space diagonal = √(l² + w² + h²).

Right circular cylinder: V = πr²h, lateral SA = 2πrh, total SA = 2πr(r + h).

Right circular cone: V = ⅓πr²h, slant ℓ = √(r² + h²), lateral SA = πrℓ, total SA = πr(r + ℓ).

Sphere: V = (4/3)πr³, SA = 4πr². The most-symmetric solid; same SA = SA of cylinder of equal r and h = 2r.

Hemisphere (half sphere): V = (2/3)πr³, curved SA = 2πr², total SA (with flat base) = 3πr².

Square pyramid: V = ⅓a²h, slant ℓ = √((a/2)² + h²), lateral SA = 2aℓ, total SA = a² + 2aℓ.

Regular tetrahedron: V = a³/(6√2), SA = √3·a², height = a√(2/3). All four faces are equilateral triangles.

Torus (donut): V = 2π²·R·r², SA = 4π²·R·r. R = major (center to tube center), r = minor (tube radius).

Ellipsoid: V = (4/3)π·a·b·c (exact), SA ≈ Knud Thomsen 1.6075 approximation (≤1.061% error worldwide).

d = √(Δx² + Δy² [+ Δz²]). Pythagorean distance in the plane or 3-space.

Midpoint = (avg of each coordinate). The point exactly between two points in 2D or 3D.

m = (y₂−y₁) / (x₂−x₁). Returns slope-intercept form y = mx + b.

a² + b² = c². Solve for hypotenuse or missing leg of a right triangle.