Math Formula Collection

📐

Complete Formula Reference

Comprehensive mathematical formulas and equations for all levels

🔢Important Mathematical Constants

Pi
π
3.14159...
Euler's Number
e
2.71828...
Golden Ratio
φ
1.61803...
Square Root of 2
√2
1.41421...
Square Root of 3
√3
1.73205...
Natural Log of 2
ln(2)
0.69314...
Natural Log of 10
ln(10)
2.30258...
Euler-Mascheroni
γ
0.57721...
📐

Algebra

Linear Equation

y = mx + b

Slope-intercept form

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a

Solutions for ax² + bx + c = 0

Distance Formula

d = √((x₂-x₁)² + (y₂-y₁)²)

Distance between two points

Midpoint Formula

M = ((x₁+x₂)/2, (y₁+y₂)/2)

Midpoint between two points

Slope Formula

m = (y₂-y₁)/(x₂-x₁)

Slope between two points

Exponential Growth

A = P(1 + r)ᵗ

Compound growth formula

Logarithm Properties

log(ab) = log(a) + log(b)

Product rule for logarithms

Change of Base

log_b(x) = log(x)/log(b)

Convert logarithm base

📏

Geometry

Area of Circle

A = πr²

Area using radius

Circumference

C = 2πr

Perimeter of circle

Area of Triangle

A = ½bh

Base times height

Pythagorean Theorem

a² + b² = c²

Right triangle relationship

Area of Rectangle

A = lw

Length times width

Volume of Sphere

V = (4/3)πr³

Sphere volume

Volume of Cylinder

V = πr²h

Cylinder volume

Surface Area of Sphere

SA = 4πr²

Sphere surface area

📊

Trigonometry

Sine

sin(θ) = opposite/hypotenuse

Basic sine ratio

Cosine

cos(θ) = adjacent/hypotenuse

Basic cosine ratio

Tangent

tan(θ) = opposite/adjacent

Basic tangent ratio

Pythagorean Identity

sin²(θ) + cos²(θ) = 1

Fundamental trig identity

Law of Sines

a/sin(A) = b/sin(B) = c/sin(C)

Triangle relationship

Law of Cosines

c² = a² + b² - 2ab cos(C)

Generalized Pythagorean theorem

Double Angle

sin(2θ) = 2sin(θ)cos(θ)

Sine double angle formula

Half Angle

sin²(θ/2) = (1 - cos(θ))/2

Sine half angle formula

∫

Calculus

Power Rule

d/dx[xⁿ] = nxⁿ⁻¹

Derivative of power function

Product Rule

d/dx[uv] = u'v + uv'

Derivative of product

Chain Rule

d/dx[f(g(x))] = f'(g(x)) · g'(x)

Derivative of composition

Fundamental Theorem

∫ₐᵇ f'(x)dx = f(b) - f(a)

Connection between derivative and integral

Integration by Parts

∫ u dv = uv - ∫ v du

Integration technique

L'Hôpital's Rule

lim[f(x)/g(x)] = lim[f'(x)/g'(x)]

Limit of indeterminate forms

Taylor Series

f(x) = Σ[f⁽ⁿ⁾(a)/n!](x-a)ⁿ

Function expansion

Arc Length

L = ∫ₐᵇ √(1 + (dy/dx)²) dx

Length of curve

📈

Statistics & Probability

Mean

x̄ = Σx/n

Average value

Standard Deviation

σ = √(Σ(x-μ)²/N)

Measure of spread

Variance

σ² = Σ(x-μ)²/N

Square of standard deviation

Z-Score

z = (x-μ)/σ

Standard score

Combinations

C(n,r) = n!/(r!(n-r)!)

Ways to choose r from n

Permutations

P(n,r) = n!/(n-r)!

Ordered arrangements

Binomial Probability

P(x) = C(n,x)pˣ(1-p)ⁿ⁻ˣ

Probability of x successes

Normal Distribution

f(x) = (1/σ√2π)e^(-(x-μ)²/2σ²)

Bell curve equation

Mathematical Operations Reference

Exponent Rules

aᵐ · aⁿaᵐ⁺ⁿ
aᵐ / aⁿaᵐ⁻ⁿ
(aᵐ)ⁿaᵐⁿ
a⁰1
a⁻ⁿ1/aⁿ

Logarithm Rules

log(ab)log(a) + log(b)
log(a/b)log(a) - log(b)
log(aⁿ)n·log(a)
log₁₀(x)log(x)
logₑ(x)ln(x)

Common Derivatives

d/dx[c]0
d/dx[x]1
d/dx[eˣ]eˣ
d/dx[ln(x)]1/x
d/dx[sin(x)]cos(x)

About Mathematical Formulas

Mathematical formulas are symbolic representations of mathematical relationships and operations. They provide a concise way to express complex mathematical concepts and enable precise calculations across various fields of study and practical applications.

This comprehensive collection covers essential formulas from algebra through advanced calculus, including geometry, trigonometry, and statistics. Each formula is presented with clear notation and practical context to help students and professionals apply them effectively in problem-solving scenarios.

Whether you're working on homework assignments, preparing for standardized tests, or applying mathematics in professional contexts, having quick access to these fundamental formulas will enhance your mathematical fluency and problem-solving capabilities.

How to Use Mathematical Formulas Effectively

1

Identify the Problem Type

Determine which area of mathematics applies to your problem and locate the relevant formula section.

2

Understand Variable Meanings

Make sure you understand what each variable in the formula represents before substituting values.

3

Substitute Carefully

Replace variables with known values, paying careful attention to signs, units, and order of operations.

4

Verify Your Result

Check that your answer makes sense in the context of the problem and has appropriate units.

Mathematical Formula Study Tips

🧠

Focus on Understanding

Learn the reasoning behind formulas, not just the formulas themselves.

🔄

Practice Rearranging

Learn to solve for different variables within the same formula.

📋

Create Formula Sheets

Make personalized reference sheets for different subjects and topics.

🎯

Work Through Examples

Practice applying formulas to various problem types and scenarios.

🔗

Connect Related Concepts

Understand how different formulas relate to and derive from each other.

✅

Double-Check Work

Always verify calculations and ensure answers are reasonable.

Frequently Asked Questions

Get answers to common questions about math formula collection