Mechanical Engineering Calculators
Precision calculation engines and interactive engineering tools for machine design, power transmission, rotordynamics, fatigue verification, and workshop manufacturing. Built on peer-reviewed mechanics and international engineering standards.
Calculate bearing L10 rating life per ISO 281 in million revolutions and operating hours with Weibull reliability and equivalent dynamic load adjustments.
L₁₀ = (C / P)ᵖ (p = 3 for ball, 10/3 for roller)Calculate geometric resultant force (F = √(Fr² + Fa²)), ISO 281 dynamic equivalent load (P = X·V·Fr + Y·Fa), and ISO 76 static equivalent load (P₀).
F = √(Fr² + Fa²) • P = X·V·Fr + Y·Fa • P₀ = max(X₀·Fr + Y₀·Fa, Fr)Determine belt pitch length, wrap angles, and center distance for open and crossed belt drives with standard V-belt matching and motor slot tension allowances.
L = 2C + (π/2)(D + d) + (D − d)² / (4C)Calculate effective belt tension (Fe = P/v = 2T/D), tight-side (T1) and slack-side (T2) dynamic tensions, centrifugal liftoff (Fc = m'v²), and shaft bearing loads.
Fe = P/v = 2T/D • (T₁ − Fc)/(T₂ − Fc) = e^(μθ)Determine standard parallel key size, shaft keyway depth (t₁), hub keyway depth (t₂), and caliper inspection depth from shaft diameter with ISO tolerance fits.
d − t₁ Caliper Check & (t₁ + t₂ > h) Radial ClearanceCalculate lifting and lowering torque, drive efficiency, thrust capacity, and self-locking conditions for square, Acme, and trapezoidal power screws.
T_R = (F·d_m/2) · [(l + π·μ·d_m·sec α) / (π·d_m − μ·l·sec α)] + T_cEstimate the fundamental lateral critical speed (first natural frequency) and resonance avoidance safety margins for simply supported and fixed rotating shafts.
ω_n = π² · √(E·I / (m·L⁴)) (Dunkerley & Rayleigh-Ritz)Compute shear stress for direct single/double shear in joints, linear torsional stress in solid and hollow circular shafts, and transverse Jourawski beam shear.
τ = F/A (Direct) • τ = T·c/J (Torsion) • τ_max = 1.5·V/A (Beam)Determine exact tap drill sizes and theoretical thread engagement percentages for ISO Metric and Unified (UNC/UNF) threads across cutting and roll forming taps.
TDS = Major Dia − (% Engagement / 100) · 1.29904 · PitchCalculate driven RPM from pulley diameters, find required pulley size for a target speed, determine speed ratio, and compute belt linear velocity.
D₁N₁ = D₂N₂ • v = πDN / 60Calculate belt linear velocity (v), required motor RPM, and sheave pitch diameter with slip factor and bending fatigue cycles.
v = π·D·N / 60 • N = 60v / (π·D)Determine roller chain link count (even pitches) and exact shaft center distance per ASME B29.1 and ISO 606 standards.
L = 2C + (N₁+N₂)/2 + (N₂−N₁)²/(4π²C)Calculate sprocket pitch diameter (P.D.), outer/root circles, chordal action velocity ripple, and drive reduction ratios.
P.D. = p / sin(180°/N) • O.D. = p·[0.6 + cot(180°/N)]Calculate torsional shear stress for solid and hollow circular shafts (τ = Tr/J), or determine the minimum shaft diameter for an allowable stress limit.
τ = 16T/(πd³) • d = [16T/(πτ)]^(1/3)Calculate the angle of twist (θ = TL/GJ) for solid and hollow shafts with material presets for shear modulus, twist rate analysis, and reverse diameter sizing.
θ = TL/(GJ) • d = [32TL/(πGθ)]^(1/4)Calculate bending stress (σ = Mc/I) for rectangular, circular, hollow circular, I-section, and custom cross-sections with section modulus output.
σ = Mc/I = M/S • S = I/cLook up clearance hole diameters, nominal drill sizes, and ISO 286 limit tolerances (H12, H13, H14) for M1.6–M100 bolts across Close, Normal, and Loose fits per ASME B18.2.8.
C = Dh − Dn • Cr = C / 2 • ISO 286 (H12/H13/H14)Look up modulus of elasticity (E), shear modulus (G), bulk modulus (K), and Poisson's ratio (ν) for 24+ carbon, alloy, structural, stainless, and tool steels with Hooke's law and Eurocode 3 fire reduction factors.
σ = E · ε • G = E / [2(1 + ν)] • δ = F·L / (A·E)Calculate mass moments of inertia (Iz, Ix, Iy) for solid and hollow cylinders with center-of-mass principal axes, density-based mass, parallel axis offsets, and rotational kinetic energy.
Iz = ½ M r² • Ix = 1/12 M (3r² + h²) • I = I_CM + M d²Compute elastic deflection, slope, shear force, and bending moment diagrams for simply supported, cantilever, fixed, and propped beams under point and distributed loads.
δ_max = P·L³ / (48·E·I) • δ_max = 5·w·L⁴ / (384·E·I)Evidence-Based Engineering Methodology
Every calculator in our mechanical suite is engineered for transparency, scientific accuracy, and auditability. We eliminate “black box” calculations by exposing full step-by-step arithmetic derivations, underlying assumptions, and authoritative standard references.
Aligned with ISO, DIN, ANSI/ASME, and AGMA standards to ensure compliance with global manufacturing specifications.
Formulated per standard references including Shigley's Mechanical Engineering Design, Beer & Johnston, and Machinery's Handbook.
Comprehensive bidirectional conversion across SI Metric and US Customary imperial units with 280+ automated unit tests.