Formula Reference

Comprehensive collection of essential formulas for mathematics, physics, and chemistry with explanations and variable definitions.

All Formulas

Mathematics

Physics

Chemistry

Mathematics Formulas

Algebra

Quadratic Formula

Algebra

Solves quadratic equations of the form ax² + bx + c = 0

x = (-b ± √(b² - 4ac)) / (2a)

Variables: a, b, c = coefficients; x = solutions

Geometry

Area of Circle

Geometry

Calculate the area of a circle given its radius

A = πr²

Variables: A = area; r = radius; π ≈ 3.14159

Volume of Sphere

Geometry

Calculate the volume of a sphere given its radius

V = (4/3)πr³

Variables: V = volume; r = radius

Pythagorean Theorem

Geometry

Relationship between sides of a right triangle

a² + b² = c²

Variables: a, b = legs; c = hypotenuse

Physics Formulas

Electricity

Ohm's Law

Electricity

Relationship between voltage, current, and resistance

V = IR

Variables: V = voltage (V); I = current (A); R = resistance (Ω)

Energy

Kinetic Energy

Energy

Energy of motion for an object with mass and velocity

KE = ½mv²

Variables: KE = kinetic energy (J); m = mass (kg); v = velocity (m/s)

Mechanics

Newton's Second Law

Mechanics

Force equals mass times acceleration

F = ma

Variables: F = force (N); m = mass (kg); a = acceleration (m/s²)

Waves

Wave Equation

Waves

Relationship between wave speed, frequency, and wavelength

v = fλ

Variables: v = wave speed (m/s); f = frequency (Hz); λ = wavelength (m)

Thermodynamics

Ideal Gas Law

Thermodynamics

Relationship between pressure, volume, moles, and temperature

PV = nRT

Variables: P = pressure; V = volume; n = moles; R = gas constant; T = temperature

Chemistry Formulas

Solutions

Molarity

Solutions

Concentration of a solution in moles per liter

M = n/V

Variables: M = molarity (mol/L); n = moles of solute; V = volume of solution (L)

Dilution Formula

Solutions

Relationship for diluting concentrated solutions

C₁V₁ = C₂V₂

Variables: C₁, C₂ = initial and final concentrations; V₁, V₂ = initial and final volumes

Acid-Base

pH Formula

Acid-Base

Measure of acidity based on hydrogen ion concentration

pH = -log[H⁺]

Variables: pH = acidity scale; [H⁺] = hydrogen ion concentration (M)

Composition

Percent Composition

Composition

Percentage of each element in a compound

% = (mass of element / total mass) × 100

Variables: % = percentage; masses in same units

Quick Reference Guide

Mathematics

• Quadratic Formula: ax² + bx + c = 0
• Circle Area: A = πr²
• Pythagorean: a² + b² = c²
• Sphere Volume: V = (4/3)πr³

Physics

• Ohm's Law: V = IR
• Kinetic Energy: KE = ½mv²
• Force: F = ma
• Wave Speed: v = fλ

Chemistry

• Molarity: M = n/V
• pH: pH = -log[H⁺]
• Dilution: C₁V₁ = C₂V₂
• Ideal Gas: PV = nRT

Formula Study Tips

Understand Variables

Learn what each symbol represents before memorizing

Practice Applications

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Check Units

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Derive When Possible

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