Mechanical & Machine Design Calculators
10 free mechanical & machine design calculators — standards-based, with formulas, worked examples, and no sign-up.
These are component-level machine design and piping checks — the calculations that live between a fluids textbook and a shop drawing. The rotating-machinery trio covers a shaft (combined bending and torsion resolved by Tresca and von Mises with Kb/Kt shock factors), the bearings that carry it (the L10 = (C/P)^p basic rating life in hours and revolutions, with the a1 reliability factor), and the springs around it (spring rate, Wahl-corrected shear stress). Vibration isolation closes the set: natural frequency, transmissibility, and the isolation percentage a mount actually achieves at your operating speed.
The pressure-and-flow tools follow the standards their industries use. Pressure vessel thickness comes from thin-wall hoop and longitudinal stress with joint efficiency and corrosion allowance, and reports MAWP. Orifice metering follows ISO 5167 with the velocity-of-approach factor. The Reynolds number tool computes Re = ρvD/μ and resolves the Colebrook-White friction factor — the input every pressure-drop calculation upstream depends on. Bolt torque converts a target preload through the K-factor to a wrench setting, pipe thermal expansion sizes loops for restrained lines, and tank volume handles the horizontal-cylinder segment geometry that defeats mental arithmetic.
All Mechanical & Machine Design Tools
Pressure Vessel Thickness Calculator
Wall thickness for cylindrical and spherical shells under internal pressure per ASME BPVC Section VIII Div 1, with corrosion allowance and MAWP.
Bolt Torque & Preload Calculator
Tightening torque and preload via T = K·F·d with ISO metric thread geometry and ISO 898-1 property classes.
Pipe Thermal Expansion Calculator
Linear thermal growth, restrained thermal stress, anchor force, and expansion-loop leg length for process and power piping.
Orifice Flow Meter Calculator
Volumetric and mass flow through a thin-plate orifice per ISO 5167, with diameter ratio, velocity-of-approach factor, pipe and throat velocities, and throat Reynolds number.
Tank Volume Calculator
Partial-fill liquid volume for vertical, horizontal, and rectangular tanks, with total capacity, percent full, and ullage in cubic metres, litres, and US gallons.
Reynolds Number & Friction Factor
Pipe-flow Reynolds number, laminar/transitional/turbulent regime, and Darcy friction factor via 64/Re or Colebrook-White and Swamee-Jain, with relative roughness and a Moody curve.
Shaft Design Calculator
Required solid circular shaft diameter under combined bending and torsion by the maximum-shear (Tresca) or distortion-energy (von Mises) theory, with fatigue stress-concentration factors and actual bending, shear and von Mises stresses.
Helical Spring Calculator
Helical compression spring design: spring index, Wahl correction factor, spring rate k = G·d⁴/(8·D³·Na), deflection, Wahl-corrected shear stress and solid length, with manufacturability warnings on spring index.
Bearing Life Calculator
Rolling-element bearing fatigue life per ISO 281: equivalent dynamic load, basic rating life L10 = (C/P)^p in million revolutions and hours for ball and roller bearings, plus reliability-adjusted life.
Vibration Isolation Calculator
Machine vibration isolator selection: natural frequency from static deflection or spring stiffness and mass, frequency ratio, damped transmissibility, and isolation efficiency, with a reverse mode giving the required static deflection for a target isolation percentage.
Frequently Asked Questions
Tresca or von Mises for the shaft check — does the choice matter?
Tresca (maximum shear) is the more conservative of the two, typically by up to about 15% for combined bending and torsion; von Mises tracks ductile test data better. Traditional shaft formulas (ASME-style) are built on Tresca. The calculator reports both so you can see the spread — if your design only passes on von Mises, you have no margin and should upsize rather than argue the criterion.
What preload should I target in the bolt torque calculator?
Common practice is 60–75% of the bolt's proof load for reusable connections, higher for permanent joints. The tool works from the tensile stress area and your target preload fraction, then applies the torque coefficient K — and K is the honest uncertainty: about 0.20 dry, roughly 0.15 lubricated, and torque scatter of ±25% is normal. When preload really matters, torque wrenches are the rough method; turn-of-nut or stretch measurement are the accurate ones.
The L10 life looks huge. Why do bearings still fail early?
L10 is a fatigue life at 90% reliability under clean, aligned, properly lubricated conditions — and most field failures are none of those: contamination, misalignment, and lubrication breakdown dominate. Treat L10 as the ceiling the load path allows, then protect it with sealing and maintenance. If you need better than 90% reliability, the a1 factor in the tool discounts the life accordingly (a1 = 0.21 at 99%).