Essential math formulas with clear explanations, variables, worked examples, and FAQs. Organized by category.
((New Value − Original Value) / Original Value) × 100
I = (P × R × T) / 100
A = P × (1 + R/100)^T
Speed = Distance / Time
Result = (Percentage / 100) × Number
Profit % = (Profit / Cost Price) × 100
Discount % = (Discount / Original Price) × 100
Average Speed = Total Distance / Total Time
a : b = c : d (if ad = bc)
LCM(a, b) = (a × b) / GCF(a, b)
x = (−b ± √(b² − 4ac)) / 2a
ax + by + c = 0
Distance = Speed × Time
ax² + bx + c = a(x − r₁)(x − r₂)
aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ / aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ
logₐ(xy) = logₐ(x) + logₐ(y), logₐ(x/y) = logₐ(x) − logₐ(y), logₐ(xⁿ) = n × logₐ(x)
aₙ = a₁ + (n − 1)d
aₙ = a₁ × rⁿ⁻¹
A = π × r²
C = 2 × π × r
A = l × w
A = ½ × b × h
a² + b² = c²
V = s³
A = s²
A = ½ × (a + b) × h
A = b × h
V = l × w × h
V = (4/3) × π × r³
V = π × r² × h
V = (1/3) × π × r² × h
SA = 4 × π × r²
SA = 2πr² + 2πrh
A = (θ/360) × π × r²
A = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2
sin θ = Opposite/Hypotenuse, cos θ = Adjacent/Hypotenuse, tan θ = Opposite/Adjacent
c² = a² + b² − 2ab × cos(C)
a/sin(A) = b/sin(B) = c/sin(C)
sin²θ + cos²θ = 1
d/dx [xⁿ] = n × xⁿ⁻¹
(fg)' = f'g + fg'
(f/g)' = (f'g − fg') / g²
d/dx [f(g(x))] = f'(g(x)) × g'(x)
∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)
Mean = (Sum of all values) / (Number of values)
Median = Middle value of sorted data
Mode = Most frequently occurring value
Range = Maximum value − Minimum value
σ = √(Σ(xᵢ − μ)² / N)
σ² = Σ(xᵢ − μ)² / N
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