Mechanical Engineering Calculators
Bearing Load Calculator
Calculate L10 bearing rating life in hours from dynamic load rating, equivalent load, and speed, with separate exponents for ball and roller bearings.
Bolt Torque Calculator
Calculate the tightening torque needed for a target clamp force from bolt diameter, preload, and nut factor K, with worked examples across common bolt sizes.
Fatigue Life Calculator
Predict cycles to failure under cyclic stress using Basquin's equation from stress amplitude, fatigue strength coefficient, and exponent, with worked examples.
Flywheel Energy Calculator
Calculate stored kinetic energy in a rotating flywheel from moment of inertia or solid disk mass and radius, with worked examples showing the effect of speed.
Gear Design Calculator
Calculate gear ratio, output speed, and output torque from tooth counts, input speed, torque, and mesh efficiency, with worked examples for reduction ratios.
Power Transmission Calculator
Convert between torque and power at a given rotational speed for shafts and drivetrains, with worked examples in kilowatts, horsepower, and newton-meters.
Pulley Ratio Calculator
Calculate belt pulley ratio and driven speed from driver and driven pulley diameters and driver rpm, with worked examples for step-up and step-down drives.
Shaft Diameter Calculator
Calculate the minimum solid shaft diameter for a given torque and allowable shear stress using the torsion formula, with a fully worked numeric example.
Spring Constant Calculator
Calculate spring constant from force and deflection, or predict it from helical coil geometry and shear modulus, with worked examples for both methods.
Stress Strain Calculator
Calculate stress, strain, or elastic modulus from force, area, and length change using Hooke's Law, with a worked example connecting all three quantities.
The Math Behind Machine Parts That Don't Fail
Mechanical engineering design questions almost always reduce to the same underlying concern: will this part survive its expected loads over its expected lifetime? Bolt torque, shaft diameter, fatigue life, and stress-strain calculations all answer versions of that question for different components. Ten calculators here cover the standard formulas used in machine design.
Popular Mechanical Engineering Calculators
Ten tools span fasteners, power transmission, and material behavior:
- Bolt Torque Calculator — calculates proper tightening torque for a bolt size and material to achieve correct preload.
- Shaft Diameter Calculator — sizes a shaft to safely transmit a given torque without excessive stress or deflection.
- Fatigue Life Calculator — estimates how many load cycles a component can withstand before fatigue failure.
- Gear Design Calculator — calculates gear ratio, tooth count, and pitch diameter relationships.
- Stress Strain Calculator — converts applied load and material properties into stress and resulting strain.
Why Fatigue Failure Happens Below a Material's Rated Strength
A component can fail well below its ultimate tensile strength if it's subjected to enough repeated load cycles — fatigue failure builds from microscopic cracks that grow slowly with each stress cycle until the remaining material can no longer bear the load, often with no visible warning before sudden failure. This is why fatigue life calculations matter most for parts under cyclic loading, like rotating shafts or vibrating components, and why a bolt correctly torqued for static strength can still fail from fatigue if it's exposed to constant vibration without adequate preload margin.
Frequently Asked Questions
Why does bolt torque matter so much if the bolt is strong enough?
Torque sets the clamping force (preload) holding a joint together; too little torque risks the joint loosening or separating under load, while too much can yield or shear the bolt, so correct torque matters independent of the bolt's raw strength rating.
Is a thicker shaft always a safer design choice?
Not necessarily the best choice — oversizing adds unnecessary weight, cost, and material, so shaft diameter calculations aim for the minimum size that safely handles the expected torque and deflection limits, not the largest feasible size.
Explore More
Working on structural rather than machine design? See the Civil Engineering Calculators, or check material cutting math in the Metalworking Calculators.