Geometry Formulas

Geometry Formula Reference

Complete collection of geometry formulas with explanations, examples, and interactive tools

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Quick Formula Reference

Essential formulas for quick lookup and reference

Triangle Basics

Area (Base × Height)

A = (1/2) × base × height

Area (Heron's Formula)

A = √[s(s-a)(s-b)(s-c)]

Perimeter

P = a + b + c

Angle Sum

∠A + ∠B + ∠C = 180°

Circle Basics

Area

A = πr²

Circumference

C = 2πr = πd

Sector Area

A = (θ/360°) × πr²

Arc Length

s = (θ/360°) × 2πr

Quadrilateral Basics

Rectangle Area

A = length × width

Square Area

A = side²

Parallelogram Area

A = base × height

Trapezoid Area

A = (1/2)(b₁ + b₂) × h

Vector Basics

Vector Addition

⃗a + ⃗b = (a₁+b₁, a₂+b₂)

Dot Product

⃗a · ⃗b = |⃗a||⃗b|cos θ

Magnitude

|⃗v| = √(x² + y²)

Unit Vector

û = ⃗v/|⃗v|

Triangle Formulas

Essential formulas for triangle calculations, solving, and analysis

Triangle Solving

Intermediate

Complete formulas for solving triangles using sine law, cosine law, and area calculations

Key Formulas:

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

Law of Cosines: c² = a² + b² - 2ab·cos(C)

Area = (1/2)ab·sin(C) = √[s(s-a)(s-b)(s-c)]

Angle Sum: A + B + C = 180°

Applications:

Triangle solving

Navigation

Engineering

Architecture

Trigonometry Formulas

Comprehensive trigonometric identities, sum/difference formulas, and reductions

Trigonometry Identity Transformations

Intermediate

Fundamental trigonometric identities and transformation formulas

Key Formulas:

Pythagorean: sin²θ + cos²θ = 1

Reciprocal: csc θ = 1/sin θ, sec θ = 1/cos θ

Quotient: tan θ = sin θ/cos θ

Co-function: sin(90°-θ) = cos θ

Applications:

Identity proofs

Equation solving

Function simplification

Calculus

Trigonometry Sum-Difference

Advanced

Sum and difference formulas for trigonometric functions

Key Formulas:

sin(A ± B) = sin A cos B ± cos A sin B

cos(A ± B) = cos A cos B ∓ sin A sin B

tan(A ± B) = (tan A ± tan B)/(1 ∓ tan A tan B)

Double Angle: sin(2θ) = 2sin θ cos θ

Applications:

Wave analysis

Oscillations

Signal processing

Physics

Trigonometry Induction

Advanced

Induction (reduction) formulas for angle transformations

Key Formulas:

sin(π ± θ) = ∓sin θ

cos(π ± θ) = -cos θ

sin(π/2 ± θ) = ±cos θ

cos(π/2 ± θ) = ∓sin θ

Applications:

Angle reduction

Period analysis

Function simplification

Proofs

📐 How to Use Geometry Formulas Effectively

Master geometry problem solving with these formula application strategies

Identify the Problem Type

Determine what you're solving for (area, perimeter, angle, side length) to choose the right formula.

Check Units & Variables

Ensure all measurements use consistent units and identify all known and unknown variables.

Verify Your Answer

Double-check calculations and ensure your answer makes sense in the context of the problem.

Need to practice using these formulas?

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