Engineering Formula Library
The equations engineers reach for, organised by mechanics, materials, fluids and electrical — every variable and SI unit spelled out. Every card links straight to a calculator that shows a worked example.
Mechanics
Force
newton · N- F — force (N)
- m — mass (kg)
- a — acceleration (m/s²)
Torque
newton-metre · N·m- τ — torque (N·m)
- F — force (N)
- r — lever length (m)
- θ — angle to the lever
Work
joule · J- W — work done (J)
- F — force (N)
- d — distance moved (m)
- θ — angle between force and motion
Kinetic energy
joule · J- E — kinetic energy (J)
- m — mass (kg)
- v — velocity (m/s)
Materials
Mechanical stress
pascal · Pa- σ — axial stress (Pa)
- F — applied force (N)
- A — cross-sectional area (m²)
Strain
dimensionless- ε — strain (no units)
- ΔL — change in length (m)
- L₀ — original length (m)
Young’s modulus
pascal · Pa- E — Young’s modulus (Pa)
- σ — stress (Pa)
- ε — strain (dimensionless)
Beam load (point load)
reaction N · moment N·m- F — point load (N)
- a, b — distance from each support (m)
- L — span, a + b (m)
- M — max bending moment (N·m)
Fluids
Pressure
pascal · Pa- P — pressure (Pa)
- F — force (N)
- A — area (m²)
Fluid (hydrostatic) pressure
pascal · Pa- P — pressure at depth (Pa)
- ρ — fluid density (kg/m³)
- g — gravity (9.81 m/s²)
- h — depth (m)
Reynolds number
dimensionless- Re — Reynolds number
- ρ — density (kg/m³)
- v — flow velocity (m/s)
- D — characteristic length (m)
- μ — dynamic viscosity (Pa·s)
Electrical
Ohm’s law
volt V · ampere A · ohm Ω- V — voltage (V)
- I — current (A)
- R — resistance (Ω)
Electrical power
watt · W- P — power (W)
- V — voltage (V)
- I — current (A)
- R — resistance (Ω)
Resistance of a conductor
ohm · Ω- R — resistance (Ω)
- ρ — resistivity (Ω·m)
- L — length (m)
- A — cross-sectional area (m²)
SI units at a glance
How to use this page
Every formula uses SI units — metres, kilograms, seconds, amperes — so results come out in the base unit shown (convert at the end if you need psi, horsepower or bar). Each formula links to a calculator on the engineering hub that shows a worked example, so you can follow the method rather than trust a black box.
Sources & references
The formulas and units on this page follow the standard definitions published by:
- NIST — the SI base and derived units and physical constants
- BIPM — the International System of Units (SI)
- Encyclopædia Britannica — the underlying physics of each quantity
Cite this page
You are welcome to quote these formulas and figures in a lesson, a forum answer, a wiki or a write-up. A link back is all we ask — it lets your reader check the figure against its source, which is the point of the page.
Tool Corner, “Engineering Formula Library”. Updated 29 July 2026. https://toolcorner.net/engineering-formulas
Every formula is stated with its symbols and its sources are linked wherever a stable public page exists, so a citation here can be traced rather than taken on trust.