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Physics & Math

Engineering Formulas

A quick-reference library of fundamental physics and mechanical engineering equations. Standardized syntax, variable definitions, and SI units.

Hooke's Law (1D)

Relates stress to strain in the linear elastic region of a material.

Governing Formula

\sigma = E \cdot \epsilon
\sigmaMPa

Normal Stress

EGPa

Young's Modulus

\epsilon-

Normal Strain

Flexural Bending Stress

Calculates the normal stress induced in a beam subjected to a bending moment.

Governing Formula

\sigma_b = \frac{M \cdot y}{I}
\sigma_bMPa

Bending Stress

MN·m

Bending Moment

ymm

Distance from Neutral Axis

Imm⁴

Area Moment of Inertia

Torsional Shear Stress

Calculates the shear stress in a circular shaft subjected to torque.

Governing Formula

\tau = \frac{T \cdot r}{J}
\tauMPa

Shear Stress

TN·m

Applied Torque

rmm

Radial Distance

Jmm⁴

Polar Moment of Inertia

Euler Column Buckling

Determines the critical compressive load that causes a long column to buckle.

Governing Formula

P_{cr} = \frac{\pi^2 E I}{(K L)^2}
P_{cr}N

Critical Load

EPa

Young's Modulus

Im⁴

Area Moment of Inertia

K-

Column Effective Length Factor

Lm

Unsupported Length

Engineering Formulas: The Foundation of Design and Analysis

Engineering is built upon fundamental physical laws expressed through mathematics. Having quick access to a reliable, standardized set of engineering formulas is essential for solving complex problems across Solid Mechanics, Fluid Dynamics, and Thermodynamics.

Importance of Unit Consistency

One of the most common sources of error in engineering calculations is unit mismatch. All formulas in this reference library are standardized around the International System of Units (SI). When using these equations, ensure that your inputs are strictly converted to base SI units (e.g., meters for length, kilograms for mass, seconds for time, and Pascals for stress or pressure) before executing the calculation.

Solid Mechanics

Solid mechanics equations form the basis of structural analysis and material science. Key formulas include Hooke's Law for linear elasticity, stress and strain derivations, and failure criteria equations like Von Mises. These are critical for determining whether a component will yield, fracture, or deform under given loads.

Fluid Mechanics & Thermodynamics

Fluid dynamics involves the study of fluids (liquids and gases) in motion. Bernoulli's equation, Reynolds number calculations, and the continuity equation are pivotal in designing piping systems, aerodynamics, and hydraulics. Thermodynamics extends this by introducing energy transfer, specific heat capacity, and thermal expansion dynamics essential for HVAC, engine design, and energy systems.

Frequently Asked Questions

What units are used in these engineering formulas?

All formulas in this reference library use the standard International System of Units (SI). Ensure your inputs are converted to standard SI units (e.g., meters, kilograms, seconds, Pascals) before calculation to avoid dimensional errors.

Which disciplines are covered in this cheat sheet?

This engineering cheat sheet currently covers fundamental equations for Solid Mechanics, Fluid Mechanics, and Thermodynamics.