Formula library for engineering problem solving
Engineering Equations and Formulas
Search 39 free equation guides for mechanics, structures, fluids, thermodynamics, electrical circuits, electromagnetism, waves, mathematics, and physics.
Find an equation by name, variable, symbol, physical quantity, discipline, or real-world application.
Equation finder
Find the right engineering equation
Browse by discipline
Engineering equation categories
Choose a category to filter the library or jump directly to a group of formulas.
Start here
Featured Engineering Equations and Formulas
Quick access to widely used formulas across mechanics, structures, fluids, heat transfer, and electrical engineering.
Complete formula index
Browse All Engineering Equations
Open a category below or search the complete index. Each link leads to a focused equation guide covering the formula and its engineering context.
Mechanics & motion
Mechanics and Motion Equations
Kinematics, Newton’s laws, force, gravity, energy, momentum, circular motion, and mechanical-power relationships.
Strength of materials
Statics and Strength of Materials Equations
Stress, strain, elasticity, bending, shear, principal stresses, spring behavior, and material deformation formulas.
Structural engineering
Structural Engineering Equations
Beam deflection and section-property equations used in structural analysis, stiffness checks, and member behavior.
Fluids & hydraulics
Fluid Mechanics and Hydraulic Equations
Pressure, velocity, conservation, pipe flow, open-channel flow, groundwater, head loss, pump scaling, and flow-regime equations.
Thermodynamics & heat transfer
Thermodynamics and Heat Transfer Equations
Gas-law, sensible-heat, thermal-expansion, and conduction equations for energy and temperature calculations.
Electrical circuits
Electrical Circuit Equations
Voltage, current, resistance, and closed-loop relationships used in DC and AC circuit analysis.
Electromagnetism & waves
Electromagnetism, Waves, and Modern Physics Equations
Electric force, electromagnetic fields, frequency, radiation, wavelength relationships, relativity, and modern-physics formulas.
Math & geometry
Mathematics and Geometry Formulas
Foundational geometry and complex-number relationships used throughout engineering analysis.
Continue your work
Related Engineering Tools and References
Move from formula selection to calculations, reference data, and discipline-specific explanations.
Use formulas correctly
How to Use an Engineering Equation
Select the equation that matches the physical model, then confirm the variables, units, sign convention, assumptions, and valid range before applying the result.
- Choose the correct model.Match the equation to the system, geometry, loading, flow regime, material behavior, boundary conditions, and required output.
- Keep units and symbols consistent.Define every variable, convert inputs into a compatible unit system, and use absolute temperature or other special units when the equation requires them.
- Check the answer.Review dimensions, signs, order of magnitude, limiting cases, and physical reasonableness; then compare with a calculator, reference, or independent method when practical.
These equation guides support learning, review, estimating, preliminary analysis, and independent checks. They do not replace applicable codes, standards, project criteria, manufacturer requirements, calibrated software, or professional engineering judgment.
Questions
Engineering Equations FAQ
Quick answers about choosing, interpreting, and applying formulas.
What are engineering equations?
Engineering equations are mathematical relationships used to describe and calculate physical behavior such as motion, force, stress, fluid flow, heat transfer, electrical circuits, waves, and material response.
How do I find the correct equation?
Start with the quantity you need to determine, identify the variables you know, and select a model whose assumptions match the physical system. Use the finder to search by equation name, variable, symbol, topic, or application.
Why do units and sign conventions matter?
An equation can be algebraically correct and still produce a wrong answer when inputs use incompatible units or inconsistent positive directions. Define the unit system and sign convention before substituting values.
What is the difference between an equation, formula, law, and theorem?
A formula is an equation arranged for a practical calculation. A physical law expresses an observed relationship, while a theorem is a mathematical statement established from defined assumptions. In engineering practice, these terms often overlap in how people search for a relationship.
Do equation pages connect to calculators?
Where a matching tool is available, equation guides can connect the underlying relationship to a calculator for faster numerical evaluation. Always review the calculator’s assumptions and inputs before using its result.
Can these equations replace final engineering design?
No. Final decisions should be checked against current codes, standards, project specifications, manufacturer information, complete boundary conditions, appropriate software, and qualified professional judgment.