Mechanical & Machine Design Calculators
33 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
Tolerance Stack-Up Calculator — Worst Case & RSS
Check signed dimension chains, worst-case clearance limits, and optional RSS assumptions with a tolerance contribution diagram and shareable setups.
Drill Point & Blind-Hole Depth Calculator
Calculate conical drill-point allowance, full-diameter versus tip depth, and remaining stock with a labeled schematic, reference tables, and exports.
Welding Heat Input Calculator
Arc welding heat input HI = 60 × V × I / (1000 × travel speed) reported in kJ/in and kJ/mm simultaneously (AWS D1.1/D1.1M:2020 §6.8.5.1 heat-input calculation / ISO TR 18491:2015 arc energy), gross per the D1.1 convention or net with the EN 1011-1:2009 Table 1 thermal efficiency factors verified against the published standard (SAW 1.0; SMAW, GMAW MIG/MAG, FCAW 0.8; GTAW/TIG 0.6), an in/min ↔ mm/min travel-speed toggle with round-then-clamp conversion, and an optional WPS-maximum pass/fail badge decided at the displayed two-decimal precision.
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.
Sine Bar Calculator (Gauge Block Stack Height)
The toolroom sine-bar identity solved both ways: gauge block stack H = L·sin θ at tenths (0.0001 in) display precision for 5-inch and 10-inch roll-center bars (100/200/300 mm sine plates via the exact-25.4 metric toggle), or the angle back from a measured stack via asin(H/L) in decimal degrees and degrees-minutes-seconds with the taller-than-the-bar domain guard — reproducing the Machinery's Handbook 5-inch constant table as derived anchors (15° → 1.29410, 30° → exactly 2.5000, 45° → 3.53553) and carrying the Handbook's above-45° accuracy caution (sensitivity falls as cos θ) with the complementary-angle setup reported automatically. Gauge-block combination for an 81-piece set deliberately out of scope.
Bolt Circle Calculator — Hole Coordinates & Chords
The Machinery's Handbook jig-boring hole-circle tables computed live: X-Y coordinates for every hole from bolt circle diameter, hole count (2–60), start angle (CCW from 3 o'clock), and an optional pattern-center offset, at machinist display precision (0.0001 in / 0.001 mm) — plus the chord between adjacent holes from 2R·sin(π/N), reproducing the Handbook's printed unit-diameter chordal factors as derived identities (5 holes → 0.58779 × BCD, 6 → exactly the radius, 8 → 0.38268 × BCD), angular pitch 360/N, symmetry sanity checks, and an inch ↔ mm toggle at the exact 25.4. Hole-pattern layout geometry only — bolt tightening is bolt-torque, concrete anchoring is anchor-bolt-design.
Torque Wrench Extension Calculator (Adapter Correction)
The corrected torque wrench setting when a crowfoot or extension adapter lengthens the lever arm: setting = target × L ÷ (L + E·cos φ) — pure moment-balance statics with the measurement convention torque-tool manufacturers publish (L from the grip center to the square-drive center, E from the drive to the fastener center) — handling in-line and angled adapters with the correction vanishing exactly at 90° (the classic sideways-crowfoot trick), a reverse mode that reveals the torque a dialed setting actually applied, inch ↔ mm length toggling and ft·lb / in·lb / N·m torque units at exact factors (12 in·lb/ft·lb; 1.3558179 N·m/ft·lb), and the calibration caveat that the wrench's accuracy tolerance applies to the corrected setting.
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.
Thread Engagement Calculator — Shear Areas & Minimum Length
Bolt-break-before-strip engagement from the FED-STD-H28/2B strength formulas at basic thread dimensions: tensile stress area At = π/4(D − 0.9743/n)² inch / π/4(d − 0.9382P)² metric (verified against ASME B1.1 published values 0.0318/0.1419/0.334 in² and ISO 898-1:2013 Table 4 — 20.1/58/84.3/157/245 mm²), external and internal thread shear areas per unit length (0.75πKn and 0.875πD at basic dims), minimum engagement LE = 2At/(ASs/Le), and the J factor scaling for weaker tapped materials — metric ↔ inch toggle with round-then-clamp and a pass/fail badge vs your available depth at displayed precision.
Speeds & Feeds Calculator — RPM, Feed Rate & MRR
Machinist speeds-and-feeds arithmetic for milling, drilling, and turning per the Machinery's Handbook relations: spindle RPM = 12·V/(π·D) from sfm and inches (1000·Vc/(π·D) metric), table feed = RPM × chip load × flutes (or × feed/rev), and material removal rate — feed × DOC × WOC milling, π/4·D²·feed drilling, 12·V·f·d turning — with an sfm ↔ m/min + in ↔ mm toggle using round-then-clamp conversion on every field. Cutting speed and chip load are user inputs from tooling data (no baked-in materials table), and RPM beyond 30,000 is flagged, never silently capped.
O-Ring Groove Calculator (AS568 Static Glands)
Static radial O-ring gland design from the AS568 dash size (30 scoped sizes across the five standard cross-sections, IDs verified against the Parker ORD 5700 AS568A size table) or a custom W/ID within 8% of a standard class: gland depth, groove width, radius, and diametral clearance from the verified Design Chart 4-1 industrial static gland table, squeeze recomputed across the W tolerance extremes against the printed band, gland fill π/4·W²/(L·G) with a worst-case ≤90% pass gate (≥10% void essential per the handbook), and installed ID stretch vs the 5% limit — all badges at displayed 0.1% precision.
Press Fit Calculator — ISO 286 Interference & Shrink Fits
Interference-fit design in two steps: ISO 286-2:2010 hole-basis fit limits for H7/k6, H7/n6 (transition), H7/p6 (light press), H7/s6 (medium drive), and H7/u6 (force fit) over 1–200 mm with every deviation verified against the published standard tables — or direct interference entry — then Lamé thick-cylinder mechanics per Shigley: interface pressure, guaranteed transmissible torque T = μpπd²L/2 and axial force at MINIMUM interference, worst-case hub/shaft hoop stresses with a yield pass/fail at displayed precision, press force, and shrink-assembly ΔT = δ/(αd) at MAXIMUM interference. Preliminary elastic sizing with steel defaults.
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.
Tap Drill Size Calculator — Metric & UNC/UNF Threads
The hole to drill before tapping: theoretical tap-drill diameter from the Machinery's Handbook percentage-of-full-thread formula (drill = major − 1.29904 × pitch × %/100, i.e. major − 0.01299 × %/TPI for inch threads or major − pitch × %/76.98 for metric) at a 50–85% engagement setting with 75% chart default, the nearest standard drill from the metric 0.1 mm-step table or the ANSI/ASME B94.11M fractional, number (#80–#1) and letter (A–Z) gauge tables with the engagement that drill actually produces, plus the closest cross-system substitute drill.
Shaft Key & Keyway Calculator (ASME B17.1)
Inch-shaft key sizing: the recommended square or rectangular key cross-section from the ASME B17.1-1967 key-size-versus-shaft-diameter schedule (all 13 rows over 5/16–6½ in verified against two concordant published reproductions with one supplier-chart typo diagnosed; epsilon-safe over/incl range lookup; keyseat depth = H/2 per the table), then the Shigley stress checks — shear τ = 2T/(d·w·L) vs the 0.577·Sy distortion-energy allowable and bearing σ = 4T/(d·h·L) vs Sy — with minimum key length per criterion, the governing one named, and a pass/fail badge on your hub length at displayed 3-decimal precision.
Roller Chain Length Calculator — ANSI Chain & Sprockets
Two-sprocket ANSI chain drive layout: chain length L = 2C/P + (N+n)/2 + (N−n)²/(4π²C/P) in pitches per the Machinery's Handbook, rounded UP to an even link count with epsilon-guarded ceilUnits rounding (even counts close on a standard connecting link — odd needs a weaker offset link), the exact center distance back-solved for the even chain C = P/4[A + √(A² − 2(N−n)²/π²)], sprocket pitch diameters PD = P/sin(180°/N), speed ratio, and chain velocity P·n·rpm/12 — with the ASME B29.1 chain-number pitch identity (#25–#240 picker, tens digits = eighths of an inch) or a custom pitch.
Punching Force Calculator (Blanking & Press Tonnage)
Sheet-metal punching and blanking force by the Machinery's Handbook press-work rule, verified against the printed text ("the pressure required equals the circumference of the hole × the thickness of the stock × the shearing strength", with non-circular cuts using the full perimeter): F = perimeter × t × S for round (πd), rectangular (2(w+h)), and custom-perimeter cuts, in lbf and US tons with exact kN and metric tonne-force equivalents, plus recommended press capacity at an adjustable safety factor. Shear strength is a user input with the Handbook's printed guidance presets (tensile substituted for margin: mild steel 60,000 → tin/lead 5,000 psi). Stripping-force estimation cut — the Handbook prints no numeric rule and online percentages are manufacturer-empirical; punch shear reduction also out of scope. NOT the ACI concrete flat-slab punching-shear check (cross-linked). Preliminary press sizing.
Spur Gear Dimensions Calculator (Module & Diametral Pitch)
Standard full-depth external spur gear geometry with each system at its own verified printed proportions: diametral pitch per ANSI B6.1-1968 (R1974) Table 2 in Machinery's Handbook (addendum 1/P, preferred dedendum 1.25/P, whole depth 2.25/P, OD = (N+2)/P, root = (N−2.5)/P, circular thickness 1.5708/P; shaved/ground variants noted) and metric module per the Handbook's DIN 867 table (addendum m, dedendum 1.157m at the printed 0.157m American-cutter clearance, whole depth 2.157m, 1.167m variant noted) — plus circular pitch, base circle D·cos 20°, center distance (N₁+N₂)/2P or m(N₁+N₂)/2 and ratio with a mating gear, the DP ↔ module toggle at the Handbook's exact 25.4 inverse (10 DP ↔ 2.54 module), and the printed 18-tooth minimum as an undercut warning. Profile shift, backlash, and internal gears out of scope.
Gear Ratio Calculator — RPM, Torque & Compound Trains
Gear-train ratios from tooth counts: stage ratio = driven ÷ driver, compound trains up to 6 stages multiplied in power-flow order, output speed = input RPM ÷ ratio, output torque = input × ratio × efficiency with the torque-multiplication factor, per-stage ratio breakdown, overdrive support, and a gear-ratio RPM chart at the 1800 RPM 4-pole motor speed covering 2:1 through 9:1.
Belt Length & Pulley Speed Calculator — V-Belt Center Distance
Two-pulley open belt drives: belt pitch length from the standard catalog formula L = 2C + π(D+d)/2 + (D−d)²/(4C) in mm and inches, driven pulley RPM from the no-slip diameter ratio N₂ = N₁·d₁/d₂, belt linear speed v = π·d₁·N₁/60 in m/s and ft/min against the classical V-belt 5–25 m/s comfort zone, and the small-pulley wrap angle 180° − 2·asin((D−d)/2C) with a hard pulley-overlap check on the center distance.
Hydraulic Cylinder Calculator — Push/Pull Force & Speed
Single-rod cylinder sizing from fluid-power fundamentals: push force = pressure × π/4·B² on the full piston, pull force = pressure × π/4·(B²−R²) on the rod-side annulus, extend speed = flow ÷ bore area and retract speed = flow ÷ annulus area, in metric (mm, bar, L/min → kN, m/s) or imperial (in, psi, gpm → lbf, in/s) with round-then-clamp unit toggling, a rod-smaller-than-bore check, and a contract-tested 200 bar force chart across the ISO 40–125 mm bores at the rod = bore/2 proportion.
Bend Allowance Calculator — K-Factor, Bend Deduction & Flat Pattern
Sheet-metal flat-pattern math from the K-factor neutral-axis model: bend allowance BA = θ·(π/180)·(R + K·T), outside setback (R+T)·tan(θ/2) for bends to 90°, bend deduction 2·OSSB − BA, and flat length = flange A + flange B − BD with a flange-covers-setback check. K-factor bounded 0.30–0.50 with the verified 0.44 air-bent mild-steel default (air bending typically 0.40–0.45); obtuse bends report the still-exact neutral-axis arc and defer the deduction to the CAD convention.
Torque, Horsepower & RPM Calculator
The shaft-power identity P = T·ω solved for any of the three quantities: HP = T(ft·lb) × RPM ÷ 5252.113 (exactly 33000/2π — why torque and HP curves cross at 5252 RPM) and kW = T(N·m) × RPM ÷ 9549.297 (exactly 60000/2π), entering imperial (ft·lb, HP) or metric (N·m, kW) values with both systems always displayed, NIST SP 811 unit bridges, and a contract-tested torque-to-horsepower chart at the 1800 RPM induction-motor speed.
Hazen-Williams Calculator — Pipe Friction Head Loss for Water
Friction head loss for water in pressure pipe via the empirical Hazen-Williams equation in SI form, h_f = 10.67·L·Q^1.852/(C^1.852·D^4.87): head loss in metres and feet, hydraulic gradient per 100 m, pressure drop in kPa and psi (ρg·h), and mean velocity with an advisory when it leaves the ~0.3–3 m/s calibration band. C coefficients verified against published tables — PVC 150, copper 140, cement-lined ductile iron 140, concrete 130, galvanized steel 120, old unlined cast iron 100 — plus a custom-C entry for aged mains.
Metal Weight Calculator — Steel, Aluminum, Plate, Bar & Tube
Weight of stock metal via W = A × L × ρ × quantity for eight shapes with exact section geometry — plate/sheet and flat bar (t·w), round bar (πd²/4), square bar (a²), hex bar ((√3/2)·f² on the across-flats size), round tube ((π/4)(OD²−ID²) with the wall-meets-in-the-middle case rejected), rectangular tube (wh−(w−2t)(h−2t)), and equal angle (t(2a−t)) — across nine alloys with datasheet-verified densities (carbon steel A36 7,850 · stainless 304 at the ASM 7,930 rather than the rounded 8,000 · aluminum 6061 2,700 · copper C110 8,940 · brass C260 8,530 · titanium Gr2 4,510 · gray iron A48 Cl.40 7,150 · zinc 7,135 · lead 11,340 kg/m³), totals per piece and per quantity in kg and lb (2.204623 lb/kg), mm/in + m/ft entry with round-then-clamp unit toggling, and a 1 × 1 m steel plate weight chart.
True Size Gauge — Wire, Drill Bit & Fastener Sizes at Actual Scale
AWG wires (ASTM B258 computed diameters), standard drills (ANSI/ASME B94.11M metric, fractional, number and letter tables), and nails or screws (ASTM F1667-pattern series, ASME B18.6.1 gauge formula) drawn at actual physical size through an ISO/IEC 7810 ID-1 credit-card screen calibration, comparing up to three items side by side with the calibration state always shown.
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%).