Quick reference for math, physics, and chemistry formulas.
31 formulas
Quadratic Formula
Mathematics
x = (−b ± √(b² − 4ac)) / 2a
Distance Formula
d = √((x₂ − x₁)² + (y₂ − y₁)²)
Midpoint Formula
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Slope of a Line
m = (y₂ − y₁) / (x₂ − x₁)
Product of Powers
Algebra
aᵐ × aⁿ = aᵐ⁺ⁿ
Power of a Power
(aᵐ)ⁿ = aᵐⁿ
Logarithm Product Rule
logₐ(xy) = logₐ(x) + logₐ(y)
Logarithm Quotient Rule
logₐ(x/y) = logₐ(x) − logₐ(y)
Logarithm Power Rule
logₐ(xⁿ) = n × logₐ(x)
Pythagorean Theorem
Geometry
a² + b² = c²
Area of a Circle
A = πr²
Circumference of a Circle
C = 2πr
Area of a Triangle
A = ½ × b × h
Area of a Rectangle
A = l × w
Volume of a Sphere
V = (4/3)πr³
Volume of a Cylinder
V = πr²h
Volume of a Cone
V = (1/3)πr²h
Sine
Trigonometry
sin(θ) = opposite / hypotenuse
Cosine
cos(θ) = adjacent / hypotenuse
Tangent
tan(θ) = opposite / adjacent
Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines
c² = a² + b² − 2ab cos(C)
Pythagorean Identity
sin²(θ) + cos²(θ) = 1
Mean (Average)
Statistics
x̄ = (Σxᵢ) / n
Variance
σ² = Σ(xᵢ − μ)² / n
Standard Deviation
σ = √(Σ(xᵢ − μ)² / n)
Z-Score
z = (x − μ) / σ
Simple Interest
Finance
I = P × r × t
Compound Interest
A = P(1 + r/n)^(nt)
Present Value
PV = FV / (1 + r)ⁿ
Future Value
FV = P × (1 + r)ⁿ
