Category
Mathematics
Mathematics formulas and calculators for unit conversion, calculus, linear algebra, and core mathematical relationships used across every engineering discipline. Includes derivative, integral, matrix, and series equations.
84Formulas
2Subcategories
Updated Jul 2026
Calculus
UCAS Calculator (UCAS Tariff Points)
Tariff Points = Σ(Size × Grade)
Calculus
Australian University Calculator (GPA to ATAR)
ATAR = f(GPA) · Percentile = g(ATAR)
Calculus
Unweighted GPA Calculator
Unweighted GPA = Σ(Grade Points × Credits) / Σ(Credits)
Calculus
Weighted GPA Calculator
Weighted GPA = Σ(Weighted Grade Points × Credits) / Σ(Credits)
Calculus
College GPA Calculator
GPA = Σ(Grade Points × Credits) / Σ(Credits)
Calculus
ACT Score Calculator
Composite Score = Average of Section Scores (1-36)
Calculus
SAT Score Calculator
Total Score = Reading & Writing Score + Math Score (400-1600)
Calculus
ATAR Calculator (Australian Tertiary Admission Rank)
ATAR = f(Scaled Subject Aggregate)
Calculus
GPA to Percentage Calculator
Percentage = (GPA / Scale) × 100
Calculus
Percentage to GPA Calculator
GPA = (Percentage / 100) × Scale
Calculus
CGPA Calculator (Cumulative Grade Point Average)
CGPA = Σ(Semester GPA × Credits) / Σ(Credits)
Calculus
GPA Calculator (Grade Point Average)
GPA = Σ(Grade Points × Credits) / Σ(Credits)
Calculus
GPA to ATAR Calculator (Australian University Converter)
ATAR = f( GPA ) · Percentile = g( ATAR )
General
Bytes to Megabytes (Binary)
MB = bytes / 1048576
General
Nautical Miles to Kilometers
km = nmi * 1.852
General
Cubic Feet to Cubic Meters
m3 = ft3 * 0.0283168
General
Fluid Ounces to Milliliters
mL = fl_oz * 29.5735
General
BTU to Joules
J = BTU * 1055.06
General
Watts to Horsepower
hp = W * 0.00134102
General
Kilowatt-hours to Joules
J = kWh * 3600000
General
Calories to Joules
J = cal * 4.184
General
Joules to Calories
cal = J * 0.239006
General
Atmospheres to Pascals
Pa = atm * 101325
General
PSI to Pascals
Pa = psi * 6894.76
General
Pascals to PSI
psi = Pa * 0.000145038
General
Meters per Second to Miles per Hour
mph = m/s * 2.23694
General
Kilometers per Hour to Miles per Hour
mph = km/h * 0.621371
General
Miles per Hour to Kilometers per Hour
km/h = mph * 1.60934
General
Hectares to Acres
acre = ha * 2.47105
General
Acres to Square Meters
m2 = acre * 4046.86
General
Square Meters to Square Feet
ft2 = m2 * 10.7639
General
Square Feet to Square Meters
m2 = ft2 * 0.092903
General
Grams to Ounces
oz = g * 0.035274
General
Ounces to Grams
g = oz * 28.3495
General
Kelvin to Celsius
C = K - 273.15
General
Celsius to Kelvin
K = C + 273.15
General
Miles to Feet
ft = mi * 5280
General
Yards to Meters
m = yd * 0.9144
General
Meters to Feet
ft = m * 3.28084
General
Feet to Meters
m = ft * 0.3048
General
Centimeters to Inches
in = cm * 0.393701
General
Inches to Centimeters
cm = in * 2.54
General
Radians to Degrees
degrees = radians * (180 / pi)
General
US Gallons to Liters
L = gal * 3.78541
General
Pounds to Kilograms
kg = lb * 0.453592
General
Miles to Kilometers
km = mi * 1.60934
General
Logarithm Change of Base Formula
log_b(x) = ln(x) / ln(b)
General
Combinations
nCr = n! / (r! * (n - r)!)
General
Permutations
nPr = n! / (n - r)!
General
Standard Deviation (Sample)
s = sqrt( sum((xi - x_bar)^2) / (n - 1) )
General
Geometric Series Sum
S_n = a1 * (1 - r^n) / (1 - r)
General
Arithmetic Series Sum
S_n = (n/2) * (a1 + an)
General
Compound Interest Formula
A = P * (1 + r/n)^(n*t)
General
Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
General
Law of Cosines
c^2 = a^2 + b^2 - 2ab*cos(C)
General
Slope-Intercept Form of a Line
y = m*x + b
General
Slope Formula
m = (y2-y1) / (x2-x1)
General
Distance Formula (Two Points)
d = sqrt((x2-x1)^2 + (y2-y1)^2)
General
Pythagorean Theorem
c = sqrt(a^2 + b^2)
General
Quadratic Formula
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
General
Vector Projection (Scalar Projection)
comp_b(a) = (a . b) / |b|
General
Vector Magnitude (Euclidean Norm)
|v| = sqrt(v1^2 + v2^2 + v3^2)
General
Cross Product of Vectors
a x b = (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1)
General
Dot Product of Vectors
a . b = a1*b1 + a2*b2 + a3*b3
General
Inverse of a 2x2 Matrix
A^-1 = (1/det(A)) * [[d,-b],[-c,a]]
General
Determinant of a 3x3 Matrix
det(A) = a(ei-fh) - b(di-fg) + c(dh-eg)
General
Determinant of a 2x2 Matrix
det(A) = a*d - b*c
General
Arc Length of a Circular Arc
L = r * theta
General
L'Hopital's Rule
lim f(x)/g(x) = lim f'(x)/g'(x) [as x -> a, for 0/0 or inf/inf forms]
General
Power Rule for Integration
Integral of x^n dx = x^(n+1)/(n+1) + C
General
Fundamental Theorem of Calculus (Definite Integral)
Integral from a to b of f'(x) dx = F(b) - F(a)
General
Chain Rule for Derivatives
d/dx[f(g(x))] = f'(g(x)) * g'(x)
General
Product Rule for Derivatives
d/dx[f(x)*g(x)] = f'(x)*g(x) + f(x)*g'(x)
General
Power Rule for Derivatives
d/dx[x^n] = n * x^(n-1)
General
Liters to US Gallons
gal = L * 0.264172
General
Kilograms to Pounds
lb = kg * 2.20462
General
Kilometers to Miles
miles = km * 0.621371
General
Degrees to Radians
radians = degrees * (pi / 180)
General
Fahrenheit to Celsius
C = (F - 32) * 5/9
General
Celsius to Fahrenheit
F = C * 9/5 + 32
Linear Algebra
Eigenvalue Equation
Av = λv
Linear Algebra
Determinant of a 2×2 Matrix
det(A) = ad − bc
Calculus
Taylor Series Expansion
f(x) = Σ f⁽ⁿ⁾(a)/n! · (x−a)ⁿ
Calculus
Fundamental Theorem of Calculus
∫ₐᵇ f'(x)dx = f(b) − f(a)