Free Engineering Calculators

GD&T Helper

14 controls, FCF builder, bonus / virtual / resultant condition (ASME Y14.5).

Tolerance Stackup

Worst-case, RSS, Monte Carlo + Cpk, contribution chart.

Limits & Fits (ISO 286)

Hole/shaft limits, clearance/interference for standard fits.

GD&T Datum Shift

Bonus tolerance plus datum shift when a datum is referenced at MMB.

Process Capability (Cpk)

Cp, Cpk, and estimated PPM defective from mean and sigma.

AQL Sampling (Z1.4)

Code letter, sample size, and OC-curve producer/consumer risk.

Reliability / MTBF

R(t)=e^(−t/MTBF), series/parallel, availability, Weibull.

Surface Finish

Ra ↔ Rq, µin, ISO N-grade (and rough Rz).

Gauge R&R

%GRR against study variation and tolerance, plus NDC.

Measurement Uncertainty

GUM budget: combine contributions, expand with a coverage factor.

Sine Bar & Gauge Blocks

Stack height for an angle, angle from a stack, block combination.

Sample Size

Parts needed for a confidence level and margin of error.

Calibration Interval

Drift to out-of-tolerance, plus the 10:1 discrimination check.

Strain Gauge Rosette

Rosette readings to principal strain, stress and von Mises.

Bolt Torque

Torque from preload (T=K·D·F), proof loads, friction presets.

Thread Reference

Tap-drill / clearance charts, tensile areas, pull-out.

Press / Shrink Fit

Lamé interference pressure, assembly force, hub stress.

Bolted-Joint Diagram

Joint stiffness, load factor, bolt vs member load, separation.

Pin / Rivet Shear

Single/double shear + bearing stress.

Eccentric Bolt Group

Elastic vector method: direct + torsional shear, critical bolt force.

Adhesive Lap Joint

Single-lap average shear stress, required overlap, factor of safety.

Retaining-Ring Groove

Groove diameter and thrust capacity (groove yield vs ring shear).

O-Ring Groove Designer

Squeeze, gland fill, groove width/depth and rod stretch.

Flange & Gasket Load

ASME-style seating vs operating bolt load and the bolt count required.

Bolt Prying Load

How much a flange lever amplifies bolt tension.

Weld Size & Weld Groups

Fillet weld throat, shear stress, size-for-load, and eccentric weld groups as a line.

Fillet Weld Capacity

AISC 360 (LRFD/ASD, directional) and EN 1993-1-8 strength, with the minimum and edge size limits.

Weld Heat Input

Arc energy vs heat input with the EN 1011-1 efficiency factor, checked against the WPS window.

Carbon Equivalent & Preheat

CE(IIW) and Pcm weldability, and the AWS D1.1 prequalified minimum preheat by thickness.

Weld Metal & Consumables

Joint cross-section to deposited metal, filler to buy, arc time and cost.

Weld Fatigue (EN 1993-1-9)

Endurance from the detail category and stress range, or the allowable range for a design life.

Snap-Fit Cantilever

Strain-based cantilever designer: taper K factor, forces, live beam.

Injection Moulding

Shot size with runners and the cooling-time equation.

Casting Shrinkage

Pattern oversize from the alloy shrinkage allowance.

Annular Snap-Fit

Permissible interference, strain and force for a bead-and-groove ring snap.

Torsional Snap-Fit

Twist angle, lever travel and torque for a torsion-bar snap.

Rib & Boss Design

Rib and boss ratios to the nominal wall, with the sink-mark verdict.

Draft & Texture

Draft needed for a given draw and texture depth, and what it costs in wall.

Self-Tapping Screw Boss

Pilot hole, boss OD, engagement and the strip-to-drive torque window.

Living Hinge

Web thickness, land length and the orientation window for a PP hinge.

Ultrasonic Weld Joint

Energy director geometry or shear-joint interference, plus the flash trap.

Feeds & Speeds

Cutting speed and chip load from the workpiece/tool-material pair, then RPM, feed rate and MRR.

Sheet-Metal Bend

Bend allowance, K-factor, deduction, flat length.

Flat Pattern (Multi-Bend)

Blank length and where every bend line lands on it, with the formed profile.

Press Brake Tonnage

Air-bend force, recommended die opening, inside radius.

Bolt Circle Layout

Hole pattern X/Y coordinates and chord spacing.

Drill-Size Lookup

Number / letter / fractional / metric drills → decimal inch & mm.

Tapping Torque

Estimated tapping torque by size, pitch and material.

Section Properties

Area, I, Z, radius of gyration for common shapes.

Beam Calculator

Deflection, moment, stress for standard load cases.

Column Buckling

Euler / Johnson critical load, slenderness, end conditions.

Fatigue

Endurance limit + Marin/notch factors; Goodman, Soderberg & Gerber.

Helical Spring

Compression, extension & torsion springs — rate, stress, deflection.

Natural Frequency

Spring-mass and static-deflection fn, damping, isolation.

Mohr's Circle

Principal stresses, max shear, von Mises from a stress state.

Pressure Vessel

Hoop / longitudinal stress, Barlow min wall, thick-wall Lamé.

Stress Concentration

Kt for holes and elliptical notches (closed-form).

Belleville Spring

Disc-spring load-deflection (Almen-Laszlo) + series/parallel stacking.

Thermal Expansion

ΔL from α·L·ΔT, constrained stress, dissimilar-material drift.

Flat-Plate Deflection

Circular plate under uniform pressure — deflection and stress.

Non-Circular Torsion

Rectangular, thin-wall closed and open sections in torsion.

Combined Loading

Axial + bending + torsion at a point: principal, von Mises, Tresca.

Impact & Drop

Drop energy, stopping force, and the dynamic amplification factor.

Shear & Moment Diagram

V and M diagrams for arbitrary loads, overhangs and cantilevers.

Load Combinations

LRFD and ASD combinations, with governing and uplift cases flagged.

Steel Beam Check

Required Z from Mu, capacity from Zx, and the L/360 check.

Wind Pressure

Velocity pressure qz from wind speed, exposure and directionality.

Snow Load

Flat and sloped roof snow load from ground snow load.

Concrete Rebar Area

As required for a rectangular section, with ACI minimum and ρ check.

Footing Bearing Pressure

Bearing pressure with moment, kern check, required area.

Retaining Wall Stability

Rankine thrust with factors of safety on overturning and sliding.

Column Base Plate

Plate area from concrete bearing and thickness from cantilever bending.

Truss Solver

Method of joints for any determinate 2D truss, signed member forces.

Capstan / Belt Friction

Rope/belt around a drum: T = T₀·e^(µθ), holding force.

Sling Angle & WLL

Leg tension from sling angle, D/d bending efficiency and working load limit.

Lift Plan & CG

Two-point lift load share about the CG, and assembly centre of gravity.

Lug / Padeye Analysis

Bearing, net-section and shear-out checks with margins.

Spur & Helical Gear

Module, pitch/outside dia, ratio, centre distance; helix angle & thrust.

Lead Screw Torque

Raise/lower torque, efficiency, self-locking check.

Belt & Pulley

Ratio, output rpm, belt speed, open-belt length.

Bearing Life (L10)

ISO 281 rating life in revolutions and hours.

Shaft Torsion

Polar J, shear stress, angle of twist, combined bending+torsion.

Key & Keyway

Key shear and bearing stress + DIN 6885 size lookup.

Gear Train Ratio

Compound train ratio, output speed and torque.

Motor Sizing

Acceleration torque from inertia, reflected J, power.

Flywheel Energy

Rotational inertia, stored energy, required J from Cs.

Gear Measurement Over Pins

Measurement over pins/wires for an external spur gear (involute).

Stepper Torque

Steps per rev, microstep resolution and incremental torque.

Chain Drive & Sprockets

Sprocket pitch diameter, chain length in links, centre distance and chordal action.

Bearing Preload

Preload force from torque or spring, and what it costs in L10 life.

Spline Torque Capacity

Side-pressure and shear torque capacity with a teeth-engagement factor.

Brake & Clutch Torque

Uniform-wear and uniform-pressure disc torque, contact pressure and stopping energy.

Mass Properties

Mass moment of inertia for common solids + composite centre of gravity.

Four-Bar Linkage

Grashof classification, output angle and transmission angle.

Rotor Balance (ISO 1940)

Permissible unbalance from an ISO G grade, mass and speed.

Critical Speed

First whirl speed from shaft geometry, plus the safe-zone verdict.

PID Tuning

Ziegler-Nichols and Cohen-Coon gains from an ultimate-gain or step test.

Second-Order Response

Overshoot, rise, peak and settling time from damping ratio and ωn.

Loop Stability (FOPDT)

Ultimate gain, ultimate period and gain margin from a FOPDT model.

Sampling & Aliasing

Nyquist limit, fold-back frequency and anti-alias filter order.

Servo Inertia Match

Reflected inertia, inertia ratio and acceleration torque through a ratio.

Motion Profile

Move time and phase breakdown for a trapezoidal or triangular move.

Bode & Stability Margins

Gain, phase and delay margin from an open-loop transfer function.

Hydraulic Cylinder

Extend/retract force and speed from bore, rod, pressure, flow.

Pipe Pressure Drop

Reynolds, friction factor, Darcy-Weisbach Δp and head loss.

Valve Cv / Kv Sizing

Liquid flow coefficient: Cv = Q√(SG/ΔP), flow ↔ ΔP, Kv.

Pump Affinity Laws

New flow/head/power from a speed change or impeller trim.

Valve Cv — Gas & Steam

Gas and saturated-steam valve sizing with choked-flow limiting.

Pipe Sizing & Reynolds

Bore for a target velocity, Reynolds number and flow regime.

Orifice & Venturi Flow

Flow from differential pressure, or the Δp a flow produces.

Tank Drain Time

Gravity drain time between two levels through an orifice.

Compressed Air System

Shaft power vs the isothermal floor, staging saving, receiver size, condensate.

Heat-Sink Resistance

Junction temp and required θsa from the series thermal path.

Heat Exchanger (LMTD)

Log-mean temperature difference, duty and required area.

Fin Efficiency

Straight-fin efficiency and heat rate from h, k and geometry.

Convection Coefficient

h from the standard Nu correlations, with range checking.

Heat Exchanger (NTU)

Outlet temperatures and duty from inlets and UA — the LMTD counterpart.

Sealed Enclosure in Sunlight

Solar gain against convection and radiation, and the hottest air a rating survives.

Heat-Up & Cool-Down Time

Thermal time constant, time to temperature, and the Biot validity check.

Steam Properties

Saturation properties from T or p, wet-steam quality, flash fraction.

Ideal Gas Process

W, Q, ΔU, ΔH and ΔS for the five standard gas processes.

Isentropic Efficiency

Real discharge temperature and work from an isentropic efficiency.

Power Cycle Efficiency

Otto, Diesel, Brayton and Rankine efficiency against the Carnot ceiling.

Combustion & Flue Gas

AFR, flue gas composition, excess air from O₂, and boiler efficiency.

Psychrometrics

Full moist-air state from any two properties — W, h, v, dew point, wet bulb.

Duct Sizing

Equal-friction round sizing, velocity check, and the rectangular equivalent.

Coil Load & SHR

Sensible / latent split and SHR from the entering and leaving air states.

Ventilation Rate (62.1)

Vbz and Voz by the 62.1 rate procedure, plus ACH and steady-state CO₂.

Pipe Insulation

Bare vs insulated loss per metre, surface temperature, critical radius.

Envelope U-Value

Assembly R and U, heat loss, and whether the inside face condenses.

Refrigeration & COP

COP, EER, kW/ton, tons, and how far the machine sits from Carnot.

AWG Wire / Ampacity

Gauge → diameter, area, copper resistance and free-air ampacity.

PCB Trace Width

IPC-2221 trace width from current, temperature rise and copper weight.

Battery Life

Runtime from capacity and load, plus watt-hours.

PWM Duty Cycle

Duty, frequency and average output voltage.

Regulator Dissipation

Linear-regulator heat and efficiency — does it need a heat sink?

Connector Derating

Per-contact current when many contacts are energized.

Cable Voltage Drop

Round-trip drop over a cable run, in volts and percent.

Fuse Sizing & I²t

Fuse rating from continuous current, plus melt time from I²t.

Buck / Boost Converter

Duty cycle, inductor ripple current and output voltage ripple.

MOSFET Power Loss

Conduction, switching and gate-drive loss with junction temperature.

Voltage Divider

Output voltage and current draw for a two-resistor divider.

LED Series Resistor

Resistor value and power from supply, forward voltage and current.

RC / RL Time Constant

τ, settling time and RC cutoff frequency.

Op-Amp Gain

Inverting and non-inverting gain from the feedback resistors.

Resistor Colour Code

Decode 4- and 5-band resistors to ohms and tolerance.

Thermistor & RTD

NTC Beta model and Pt100/Pt1000 RTD — resistance ↔ temperature.

ADC Resolution

LSB size, counts, ideal SNR and ENOB for a given bit depth.

Encoder Resolution

Quadrature counts, angular/linear resolution and output frequency.

Load Cell / Strain Bridge

Bridge output in mV, required amplifier gain and ADC resolution.

4–20 mA Loop

Current ↔ engineering value, sense resistor and max loop resistance.

Crystal Load Capacitors

Load capacitor value from crystal CL and stray capacitance.

AC Impedance & Resonance

Series/parallel RLC impedance, phase, resonance, Q and bandwidth.

Filter Response

Cutoff, gain, phase and the order needed for a target attenuation.

Lens Focal Length

Focal length from sensor, field of view and working distance.

Camera Resolution

mm per pixel, smallest resolvable feature, pixels on target.

Depth of Field

DOF from f-number and magnification, plus the diffraction limit.

Motion Blur & Exposure

Blur in pixels from line speed, and the exposure that avoids it.

Combine Noise Levels

Add sources, subtract background, average readings on an energy basis.

Sound Power & Distance

Sound power to pressure at distance; inverse-square attenuation.

Noise Exposure Dose

Daily dose, 8-hour TWA and allowed time under OSHA or NIOSH rules.

Enclosure & Barrier TL

Mass-law panel TL, and what a gap does to an enclosure.

Reverberation (RT60)

Sabine RT60 from room volume and absorption; treatment needed.

Miles' Equation

Random-vibration Grms and 3σ inertia load from a flat PSD.

Margin of Safety

MS = allowable/(applied × FS) − 1, the aerospace pass/fail number.

Rivet Joint Allowables

Rivet shear vs sheet bearing — which governs the joint.

Panel Buckling

Critical compression stress of a flat plate by edge condition.

Shock Response (SRS)

Half-sine pulse maximax response and amplification factor.

Plate Panel (Rectangular)

Plating bay under pressure: stress, deflection and the thickness it asks for.

Displacement & Hydrostatics

Displacement, draft, TPC, reserve buoyancy and the Froude speed regime.

Stiffener & Frame Sizing

Line load, design moment and the section modulus with the plating as a flange.

Initial Stability (GM)

KB, BM, GM, free-surface loss, heel from a weight or a beam wind, roll period.

Sacrificial Anode Sizing

Cathodic protection to DNV-RP-B401: current demand, anode mass, output and count.

Resistance & Powering

ITTC-57 friction, the allowances, wave and air drag, and the power it all takes.

Triangle Solver

Right-triangle and oblique (SSS/SAS) solutions.

Material Properties

E, density, yield, UTS, CTE for common metals & plastics.

Material Selector

Filter & rank 74 materials by specific strength/stiffness; compare up to 4 side by side.

Unit Converter

Engineering unit conversions (force, pressure, torque…).

Hardness Converter

HRC / HB / HV ↔ approximate tensile strength.

Material Weight

Mass and cost from shape, size and material density.

Engineering Calculators

Tolerancing & GD&T