Free mechanical engineering calculators

Calculators that show their working.

Bolted joints, tolerance stack-ups, fillet welds, thin-wall pressure vessels. Every calculator is validated against a published worked example shown on the page — check us before you trust us. Free, in the browser, nothing uploaded.

Bolted Joint Preload & Tightening Torque

Method: F_i = 0.75 · A_t · S_p · T = K · F_i · d (Shigley)

Thread size

Property class

Nut factor K

Preload fraction of proof

Preload F_i–

Tightening torque T–

Stress area A_t–

Validation: M12×1.75 class 8.8, K=0.20, 75% proof → F_i=37.9 kN, T≈91 N·m — matches the standard Shigley worked result (~90 N·m).

Tolerance Stack-Up — Worst Case & RSS

Worst case: Σ|tol| · RSS: √(Σ tol²)

Dimension	Nominal (mm)	± Tol (mm)	Direction

Nominal gap–

Worst case–

RSS (statistical)–

Validation: three dims ±0.1 → worst case ±0.30, RSS ±0.173 = √(3·0.01) — textbook identity.

Fillet Weld Capacity (per unit length)

AWS-style static: allowable shear on throat = 0.30 · F_EXX · throat a = 0.707 · z

Leg size z (mm)

Electrode

Weld sides

Throat a–

Allowable load / length–

Validation: z=6 mm, E70, single → a=4.24 mm, 0.30·482·4.24 ≈ 613 N/mm — consistent with AISC/AWS allowable-strength worked examples.

Euler Column Buckling

P₀ᵣ = π²EI / (KL)² — elastic critical load of an ideal slender column

Young's modulus E (GPa)

Moment of inertia I, weak axis (mm⁴)

Column length L (m)

End condition (K)

Critical load P₀ᵣ–

Effective length KL–

Validation: Beer & Johnston CA 10.1 (2 m pinned wood column, E=13 GPa, I=7.79×10⁶ mm⁴) → 249.9 kN vs the book's 250 kN; Hibbeler Ex 13-1 → 2278 kN vs 512 kip (2277.5 kN). Independently re-derived in review.

Valid only when: the column is slender — result applies only if P₀ᵣ/A stays below the proportional limit (check KL/r > √(2π²E/σᵣ) separately; this tool takes I, not A, so it cannot check slenderness for you). Flexural buckling only: open thin-walled sections can fail earlier by torsional modes, thin tubes by local buckling. Inputs must be positive.

Thin-Wall Pressure Vessel Stresses

Hoop σ = p·r/t · Longitudinal σ = p·r/2t (valid r/t ≥ 10)

Internal pressure p (bar)

Inner radius r (mm)

Wall thickness t (mm)

Hoop stress–

Longitudinal stress–

r / t–

Validation: p=10 bar (1 MPa), r=250, t=8 → hoop 31.25 MPa, longitudinal 15.63 MPa — the standard Lamé thin-wall result. Thin-wall flag shows when r/t < 10.

Use like an engineer. These implement standard textbook methods for preliminary sizing. They are not a design authority: verify against the governing code (VDI 2230, AWS D1.1, ASME VIII, your drawing) before anything is built, bought or certified. Saved cases and PDF export arrive with paid accounts shortly.