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

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Understand Variables

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Derive When Possible

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