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The 100 Formula Library
The biggest engineering cheat sheet on the web.
Normal Stress
σ = F / A
Force / Area
Strain
ε = ΔL / L
Change in Length / Length
Young's Modulus
E = σ / ε
Stress / Strain
Max Moment (Point)
M = PL / 4
Simply supported beam
Max Moment (Dist.)
M = wL² / 8
Uniform distributed load
Void Ratio
e = Vv / Vs
Vol. voids / Vol. solids
Porosity
n = e / (1+e)
Relation to void ratio
Shear Strength
τ = c + σ tan(φ)
Mohr-Coulomb
Manning's Eq
V = (1/n) R⅔ S½
Open channel velocity
Max Deflection
δ = PL³ / 48EI
Point load center
Slope (Gradient)
m = (y₂-y₁) / (x₂-x₁)
Rise over Run
Concrete Density
ρ ≈ 2400 kg/m³
Standard reinforced
Slope Correction
C = L(1 - cosθ)
Surveying error
Ohm's Law
V = I × R
Voltage definition
DC Power
P = V × I
Watts
Power Loss
P = I² × R
Heat dissipation
Series Resistors
R = R₁ + R₂
Total Resistance
Parallel Resistors
1/R = 1/R₁ + 1/R₂
Inverse sum
Frequency
f = 1 / T
Hertz vs Period
Capacitance
C = Q / V
Charge / Voltage
Capacitor Energy
E = ½ C V²
Stored energy
Inductor Voltage
V = L (di/dt)
Change in current
AC Power (1-ph)
P = VI cos(φ)
Real Power
3-Phase Power
P = √3 VL IL cosφ
Star/Delta systems
Resonance Freq
f = 1 / 2π√LC
LC Circuit
Transformer
Np/Ns = Vp/Vs
Turns ratio
Coulomb's Law
F = k q₁q₂ / r²
Electric force
Torque
τ = F × d
Moment of Force
Horsepower
HP = T×RPM/5252
Imperial units
Kinetic Energy
KE = ½ m v²
Motion energy
Potential Energy
PE = m g h
Height energy
Gear Ratio
GR = N_out / N_in
Teeth count
Hooke's Law
F = -k x
Spring constant
Thermal Expansion
ΔL = α L ΔT
Length change
Pressure
P = F / A
Force / Area
Belt Speed
v = π D n / 60
Pulley velocity
Work
W = F × d
Force x Distance
Friction
Ff = μ N
Normal force coeff
Stress Conc.
σ_max = K σ_nom
K factor
Hoop Stress
σ = Pd / 2t
Thin walled cylinder
Flow Rate
Q = A × v
Area x Velocity
Hydrostatic Press.
P = ρ g h
Fluid depth
Bernoulli
P + ½ρv² + ρgh
Conservation of energy
Reynolds Num
Re = ρvL / μ
Laminar vs Turbulent
Buoyancy
Fb = ρ g V
Archimedes
Darcy-Weisbach
hf = f (L/D) (v²/2g)
Pipe head loss
Shear Stress
τ = μ (du/dy)
Newtonian fluid
Mach Number
M = v / c
Speed / Speed of sound
Hydraulic Diam
Dh = 4A / P
Non-circular pipes
Pump Power
P = ρ g Q h / η
Hydraulic power
Specific Heat
Q = mcΔT
Heat transfer
Ideal Gas Law
PV = nRT
State equation
Carnot Eff.
η = 1 - Tc/Th
Max theoretical eff.
Conduction
Q = -kA (dT/dx)
Fourier's Law
Convection
Q = hA(Ts - Tf)
Newton's Law
Radiation
Q = εσA(T⁴-Tc⁴)
Stefan-Boltzmann
Entropy
ΔS = Qrev / T
Disorder measure
Enthalpy
H = U + PV
Total heat content
Work (Gas)
W = P ΔV
Constant pressure
Pythagoras
a² + b² = c²
Right triangle
Circle Area
A = π r²
Area
Circumference
C = 2 π r
Perimeter
Cylinder Vol
V = π r² h
Volume
Sphere Vol
V = 4/3 π r³
Volume
Quadratic Eq
x = (-b±√Δ)/2a
Find roots
Sine Rule
a/sinA = b/sinB
Triangles
Cosine Rule
c²=a²+b²-2abCosC
Triangles
Power Rule
d/dx(xⁿ) = nxⁿ⁻¹
Derivative
Power Rule Int
∫xⁿdx = xⁿ⁺¹/n+1
Integral
Log Rule
log(ab)=log(a)+log(b)
Logarithm
Euler's Formula
e^ix = cosx+isinx
Complex numbers
Newton's 2nd
F = m a
Force law
Gravity
F = G m₁m₂/r²
Universal gravity
Velocity
v = v₀ + at
Constant accel
Distance
x = x₀+v₀t+½at²
Kinematics
Momentum
p = m v
Mass x Velocity
Density
ρ = m / V
Material property
Wave Speed
v = f λ
Freq x Wavelength
Energy (Rel)
E = m c²
Einstein
Byte
1 Byte = 8 bits
Data unit
AND Gate
Y = A . B
Logic Multiply
OR Gate
Y = A + B
Logic Add
Shannon Limit
C=B log₂(1+S/N)
Max data rate
Binary Search
O(log n)
Time complexity