Free engineering calculators
Calculators for students, tradespeople and engineers, with every step of the working shown. They use fixed textbook formulas, so the working does not need checking: what matters is the numbers you type in. No account needed. Metric, US and UK imperial units.
Conveying and bulk handling
- Belt Conveyor Power and Tension Calculator
Estimate the belt conveyor effective tension, drive power and drive pulley tension ratio from capacity, length, lift and friction factor. - Screw Conveyor Capacity and Power Calculator
Estimate the capacity and drive power of a screw conveyor from the flight diameter, pitch, speed, fill factor and bulk density. - Air Cannon Calculator: Air Consumption and Compressor Size
Calculate the free air used by air cannons from tank size, firing pressure and shots per hour, and the compressor delivery needed. - Screw Conveyor Sizing Calculator: Capacity, Speed and Drive Power by the Handbook Method
Size a screw conveyor: capacity from trough loading and slope, the recommended speed for the material, and the motor power by the engineering handbook method.
Electrical
- Three-Phase Power and Motor Current Calculator
Calculate three-phase kVA, kW, kvar and line current, or the current a motor draws from its shaft power, voltage, power factor and efficiency.
Fluids and piping
- Orifice and Nozzle Flow Calculator
Calculate the flow rate through an orifice or nozzle from its diameter, pressure drop, fluid density and discharge coefficient. - Pipe Thermal Expansion Calculator
Calculate the thermal expansion of a pipe run between anchors for carbon steel, stainless steel, copper or aluminium. - Pipe Pressure Drop and Pump Power Calculator (Water)
Calculate pipe friction loss, total head and pump power for water in a pipe using the Darcy-Weisbach equation. - Steel Pipe Sizes: Outside Diameter, Wall, Bore and Mass
Look up the outside diameter, wall thickness, inside diameter, flow area and mass per metre of standard steel pipe, from DN6 to DN600 in Schedules 10 to 160, STD, XS and XXS. - Hydraulic Cylinder Force and Speed Calculator
Calculate the push and pull force, speed, stroke time and hydraulic power of a double-acting hydraulic cylinder. - Air Receiver Sizing Calculator: Time to Fall or Fill
Calculate how long a compressed-air receiver takes to fall between two pressures at a given consumption, or to fill with a compressor. - Pump and Fan Affinity Laws Calculator
Calculate how pump or fan flow, head or pressure and power change with speed, impeller diameter and air density. - NPSH Calculator: Net Positive Suction Head and Cavitation Margin
Calculate the net positive suction head available at a pump and the margin over the NPSH required, to avoid cavitation. - Pump Head Calculator: Total Head, Power and NPSH from Gauge Readings
Calculate the total head of a pump from the suction and discharge gauge readings, with the velocity heads and gauge height, plus the power and the NPSH available. - Fluid Mechanics Calculator: Pressure, Buoyancy, Jets, Bernoulli, Viscosity and Stokes
Pressure at a depth, U-tube manometer, buoyancy, Torricelli jet, continuity and Bernoulli with Reynolds number, viscous shear force and Stokes terminal velocity. - Steam Pipe Sizing Calculator
Calculate the steam pipe size from the steam flow, pressure and a target velocity, with the nearest standard pipe and the actual velocity. - Pipe Fittings Loss Calculator (K Values)
Count the elbows, tees and valves in a pipe line to get the total loss coefficient K and the head and pressure loss. - Control Valve Kv and Cv Sizing Calculator
Calculate the flow coefficient Kv and Cv a valve needs to pass a liquid flow at a given pressure drop. - Pump Curve and System Curve Calculator: Operating Point
Find where a pump runs: the intersection of its head-flow curve with the system curve of static head plus friction. Plots both curves.
Machine design
- Bolt Stress and Tightening Torque Calculator
Calculate the tensile stress area, bolt stress and tightening torque of a metric bolt from its diameter, pitch and load. - Gear Train Calculator: Speed Ratio, Output Speed and Torque
Calculate the speed ratio, output speed, output torque and efficiency of a one or two stage gear train from the tooth counts. - Helical Compression Spring Calculator: Rate, Deflection and Stress
Calculate the spring rate, deflection and shear stress of a helical compression spring from the wire diameter, coil diameter and coils. - Rolling Bearing Life Calculator (L10)
Calculate the basic rating life L10 of a ball or roller bearing from its dynamic load rating, load and speed. - Flange Bolt Calculator: Preload, Gasket Sealing Stress and Torque
Calculate the bolt preload at a percentage of proof strength, the gasket sealing stress and the tightening torque of a bolted flange. - Drawing Check List under AS 1100
A free check list of the main AS 1100 technical drawing requirements: title block, projection, scale, parts list, tolerances and more, with the clause for each. - Motor Sizing Calculator from Load Torque and Speed
Calculate the motor power needed from the load torque and speed, with gearbox efficiency, service factor and the next standard motor size. - Bolt Group Calculator: Force on Each Bolt
Calculate the direct and torsional shear on each bolt of a group loaded off-centre, and find the most heavily loaded bolt. - Fillet Weld Calculator: Throat Stress and Length
Calculate the throat stress in a fillet weld, the factor against an allowable stress, and the weld length or leg size needed. - Compression Spring Solid Height and Buckling Calculator
Calculate the solid height, deflection to solid, spring rate and buckling check of a helical compression spring from its coil data. - Extension Spring Calculator: Rate, Extension and Stress
Calculate the rate, extension under a force and body shear stress of a helical extension spring with initial tension. - Torsion Spring Calculator: Rate, Angle and Stress
Calculate the spring rate per turn, angle of deflection and bending stress of a helical torsion spring. - Springs in Series and in Parallel Calculator
Calculate the combined stiffness of up to four springs joined in series or in parallel, and the deflection under a force. - ISO 286 Limits and Fits Calculator: Hole and Shaft Tolerances, Clearance and Interference
Find the size limits of a hole and shaft from their ISO 286 tolerance classes such as H7 and g6, with the clearance or interference, fit type and a tolerance zone diagram.
Maths and data
- Simultaneous Equations Solver (Matrix Method, 2 to 8 Unknowns)
Solve 2 to 8 simultaneous linear equations by Gaussian elimination with partial pivoting. Every row operation shown. - Statistics Calculator: Mean, Standard Deviation and Line of Best Fit
Calculate the mean, median, standard deviation and range of a list of numbers, or a least-squares straight-line fit to x and y pairs. - Volume, Surface Area and Mass of Solid Shapes Calculator
Calculate the volume, surface area and mass of a cylinder, cone, sphere, box, cone frustum or tube from its dimensions and density. - Calculus Calculator: Derivative, Integral and Root of a Function
Type a function of x and get its value, slope (derivative), the area under it (definite integral) or a root, calculated numerically.
Mechanics and motion
- SUVAT Calculator: Straight-Line Motion with Constant Acceleration
Calculate final speed and distance for straight-line motion with constant acceleration (SUVAT equations), with the working shown. - Projectile Motion Calculator
Calculate the range, maximum height and time of flight of a projectile from its launch speed, angle and height. No air resistance. - Natural Frequency and Damping Calculator (Single Degree of Freedom)
Calculate the natural frequency, damping ratio and damped frequency of a mass-spring-damper system. - Force, Work, Energy and Power Calculator
Calculate acceleration from force and mass, work and power, kinetic and potential energy, and the torque, power and centrifugal force of a rotating shaft. - Flywheel Inertia and Energy Calculator
Calculate the moment of inertia, kinetic energy and energy released by a flywheel (solid disc or ring) and its rim speed.
Pools, air-conditioning and heat
- Swimming Pool Circulation Calculator: Flow, Filter and Pipe Sizes
Calculate the circulation flow, filter area, suction and return pipe sizes and backwash flow for a swimming pool from its volume and turnover time. - Swimming Pool Heat Loss and Heater Size Calculator (Indoor and Outdoor)
Calculate where an indoor or outdoor swimming pool loses heat, the heater or heat pump needed to hold the temperature, and the heat-up time. - Indoor Pool Hall Dehumidification and Ventilation Calculator
Calculate how much water an indoor pool evaporates, the outdoor air or dehumidifier needed to control humidity, the heat load of that air and a condensation check. - Refrigeration Cycle Calculator: COP, Compressor Power and p-h Diagram
Calculate the vapour-compression cycle for R134a, R32, R410A, R290, ammonia and others: states, mass flow, compressor power, COP, heat rejected and a p-h chart, every step shown. - Cooling and Heating Coil Load Calculator: Sensible, Latent and Condensate
Calculate the total, sensible and latent load of an air cooling coil, the condensate removed and the sensible heat ratio, or the load of a heating coil, with every step shown. - Air Mixing Calculator: Return Air and Outdoor Air
Calculate the temperature, humidity ratio, relative humidity and enthalpy when two air streams mix, such as return air and fresh air, with a fog warning. - Heat Pump and Chiller COP Calculator: Capacity and Running Cost against Outdoor Temperature
Estimate the COP, capacity and running cost of a heat pump or chiller as the outdoor temperature changes, with graphs of COP and capacity against outdoor temperature.
Reference and conversion
- Steel Weight Calculator: Plate, Bar and Tube
Calculate the mass of steel plate, flat bar, round bar and hollow sections from the dimensions, length, quantity and density. - Engineering Unit Converter (Metric, US and UK Imperial)
Convert pressure, force, power, flow, mass and more between metric, US and UK units, with the US short ton and UK long ton kept apart. - Typical Material Properties: Steel, Stainless, Aluminium, Copper
Typical density, modulus, yield and tensile strength, thermal expansion and conductivity of mild steel, stainless, aluminium, copper and more.
Structures and strength
- Beam Calculator: Reactions, Bending Moment, Stress and Deflection
Free beam calculator for cantilever and simply supported beams. Reactions, maximum bending moment, stress and deflection with every step shown. - Axial Stress, Strain and Elongation Calculator
Calculate axial stress, strain, elongation and factor of safety for a bar in tension or compression. Free, with every step shown. - Shaft Torsion Calculator: Shear Stress and Angle of Twist
Calculate the shear stress and angle of twist of a solid round shaft under torque, with a factor of safety and the diameter needed. - Principal Stress and Mohr's Circle Calculator with von Mises
Find principal stresses, maximum shear stress, the principal angle and the von Mises stress from plane stress components. - Euler Column Buckling Calculator
Calculate the Euler critical buckling load, slenderness ratio and critical stress of a column, and what would make it safe. - Section Properties Calculator: Area, Second Moment and Section Modulus
Calculate area, second moment of area, section modulus and radius of gyration for rectangles, circles and hollow sections. - Thin-Walled Pressure Vessel Stress Calculator
Hoop and longitudinal stress in a thin-walled cylinder or sphere under internal pressure, with factor of safety and wall thickness needed. - Plastic Section Modulus and Shape Factor Calculator
Calculate the elastic and plastic section modulus, shape factor, first-yield moment and plastic moment for rectangles, circles, hollow sections and I-sections. - Elastic Constants Calculator: E, G, K and Poisson's Ratio
Calculate Young's modulus, shear modulus, bulk modulus and Poisson's ratio from any two, with the axial, lateral and volume strain under a stress. - Beam Analysis Calculator with Shear Force and Bending Moment Diagrams
Free beam calculator for multiple point and uniform loads. Reactions, shear force diagram, bending moment diagram and deflection for simply supported, cantilever, fixed and propped beams.
Thermodynamics and heat
- Ideal Gas Law Calculator: Mass and Density
Calculate the mass and density of a gas from its pressure, volume and temperature using the ideal gas equation. - Carnot Efficiency Calculator: Heat Engine, Refrigerator and Heat Pump
Calculate the Carnot efficiency of a heat engine and the Carnot COP of a refrigerator or heat pump between two temperatures. - Heat Conduction Through a Two-Layer Wall Calculator
Calculate the heat flow through a two-layer wall or insulated surface from the temperatures, thicknesses and thermal conductivities. - Steam Properties and Pipe Velocity Calculator
Look up saturated steam temperature, specific volume and latent heat from the gauge pressure, and the steam velocity in a pipe. - Steam Tables and Property Tables Calculator with Interpolation
Look up saturated, superheated and compressed-liquid steam, R134a, ammonia, air and gas properties. See the table rows and the interpolation. - Heat Exchanger LMTD Calculator
Calculate the log-mean temperature difference and the heat transfer area for a counter-flow or parallel-flow heat exchanger. - Flash Steam Calculator
Calculate the percentage and the amount of flash steam produced when hot condensate drops to a lower pressure. - Pipe Insulation Heat Loss Calculator
Calculate the heat loss per metre from an insulated pipe, the surface temperature, and the saving compared with a bare pipe. - Psychrometric Calculator: Humid Air Properties
Calculate the humidity ratio, dew point, wet-bulb temperature, enthalpy and specific volume of moist air from temperature and relative humidity.
Workplace health and safety
- Risk Matrix Calculator (5x5): Likelihood x Consequence
Rate a workplace risk on a standard 5x5 matrix: choose likelihood and consequence, get the score and band, then rate it again after your planned controls. - Noise Exposure Calculator: Daily LAeq,8h and Noise Dose
Work out the 8-hour equivalent noise level and daily noise dose from up to three noise levels and times, and compare it with the exposure standard you enter.
How these calculators are checked
Every calculator uses a fixed textbook formula, worked out step by step, so the same numbers always give the same answer. After every update the site runs every calculator and compares 173 results with answers worked out independently by hand, and the update is not released if any of them differ. What decides whether an answer is useful is the numbers you type in, so use the calculators only if you are competent to choose them, and have anything safety-critical checked by a qualified engineer.
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