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🔬 ScienceFree
Displacement calculator
A body starting at 10 m/s and speeding up at 2 m/s² for 5 seconds ends 75 metres from where it began.
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Drift velocity calculator
A current of 1.6 A through a 1 mm² wire holding 10²⁸ conduction electrons per cubic metre drifts at only 1 millimetre per second.
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Earth curvature calculator
Over 20,000 m the surface falls a few tens of metres, but from an eye height of 1.7 m part of that bulge is still in view.
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Heat exchanger effectiveness-NTU calculator
A counterflow exchanger with an NTU of 1 and a capacity ratio of 0.5 delivers a little over half of the maximum possible heat transfer.
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Elastic constants calculator
For steel, a Young's modulus of 200 GPa and a Poisson's ratio of 0.3 are enough to fix the shear and bulk moduli too.
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Electric motor torque calculator
A 1.5 kW motor turning at 1,500 rpm delivers about 9.549 newton-metres at the shaft. Enter the power in watts and the speed in revolutions per minute to get the…
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Electrical mobility
A carrier drifting at 5 centimetres per second in a field of 100 volts per metre has a mobility of 0.0005 square metres per volt-second.
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E=mc² calculator
One kilogram at rest holds nearly 9 × 10¹⁶ joules, its mass times the speed of light squared. Enter a rest mass in kilograms to get its rest energy in joules…
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Energy to wavelength calculator
A photon carrying 10⁻¹⁹ joules has a vacuum wavelength of about 2 micrometres. Enter a photon energy in joules to get its wavelength in metres, worked out from…
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Escape velocity calculator
Leaving the Earth, with 5.972 × 10²⁴ kg and a radius of 6,371,000 m, takes a little over 11 kilometres per second.
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Excess electrons calculator
A charge of −3.2 × 10⁻¹⁸ coulombs is 20 extra electrons when you use the classroom value of 1.6 × 10⁻¹⁹ coulombs.
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Exoplanet calculator
Around a star of one solar mass, a planet at 1 AU completes its orbit in 365.25 days. Enter the star's mass plus either the orbital period in days or the…
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Fan airflow calculator
A 0.4 m fan at 1500 rpm pushes air forward at 10 metres per second in the ideal model, a little over 1 cubic metre per second.
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Fermi level calculator
Copper, with about 8.47 × 10²⁸ conduction electrons per cubic metre, has a Fermi energy near 7 electronvolts.
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Flow rate calculator
A section of 0.01 square metres with fluid moving at 1.5 metres per second carries 0.015 cubic metres per second.
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Foot-pounds of energy calculator
Muzzle energy in foot-pounds is the weight in grains times the speed in feet per second squared, divided by 450240, the formula printed beside factory load…
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Free fall distance calculator
An object dropped from rest falls 19.6 metres in 2 seconds when gravity is 9.8 m/s², with air resistance ignored.
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Free fall height calculator
If a stopwatch shows a 2-second drop under 9.8 m/s² of gravity, the object was released 19.6 metres up.
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Frequency of light calculator
A 1-metre wavelength in vacuum gives 299,792,458 Hz, and a 500 nm green line comes out near 6 × 10^14 Hz, the scale of visible light.
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Friction coefficient calculator
Divide the friction force by the normal force and get the coefficient μ: 20 N of friction against 50 N of normal force gives 0.4.
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Friction factor calculator
With a Reynolds number of 100,000 and a relative roughness of 0.0002, the Darcy friction factor is 0.019003236842, in turbulent flow.
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Froude number calculator
Water moving at 2 m/s with a depth of 1 m under Earth's 9.81 m/s² gives a Froude number of 0.6385508568, a subcritical flow.
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Gear ratio RPM calculator
A 1000 rpm motor turning a 20-tooth gear that drives a 40-tooth gear gives a ratio of 2 and 500 rpm at the output.
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Gay-Lussac's law calculator
Heat a sealed sample at 1 atm from 300 K to 600 K and its pressure doubles to 2 atm. Give the starting pressure in any unit and both temperatures in kelvin; the…
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Generator power calculator
A 230 V single-phase generator delivering 10 A at a power factor of 0.8 gives 1840 W, or 1.84 kW, of real power.
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Ground speed calculator
At 250 knots true airspeed with a 40-knot tailwind, ground speed is 290 knots; turn that wind into a headwind and it drops to 210.
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Hair diffraction calculator
A 500 nm laser, a screen 2 m away and dark fringes 10 mm apart give a hair diameter of 0.0001 m, or 100 micrometres.
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Hall coefficient calculator
12 mV of Hall voltage across a strip half a millimetre thick, at 2 mA in a quarter-tesla field, gives a Hall coefficient of 0.012 m³/C.
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Heisenberg uncertainty calculator
Confine a particle to 10^-10 m, an atomic scale, and its momentum spread can be no smaller than about 5 × 10^-25 kg·m/s.
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Helical coil inductance calculator
Ten turns on a 0.0254 m radius spread over 0.0508 m, a 1-inch by 2-inch air coil, give 3.44827586207 µH.
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Helmholtz resonator calculator
A 1.87-litre cavity with a neck 3.14 cm² in area and 5 cm long resonates at about 100 Hz in air at 343 m/s.
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Hoop stress calculator
A pipe at 1 MPa with a 0.2 m bore and a 5 mm wall carries a hoop stress of 20,000,000 Pa, the circumferential pull that tries to split it along a seam.
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Hubble's law calculator
A galaxy 100 megaparsecs away recedes at 7000 km/s when the Hubble constant is 70 km/s per megaparsec.
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Hydraulic gradient calculator
Heads of 20 m and 16 m at two wells 100 m apart give a hydraulic gradient of 0.04, with groundwater moving from the first well toward the second.
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Hydraulic radius calculator
A section with 2 m² of flow area and 4 m of wetted perimeter has a hydraulic radius of 0.5 m. Divide area by wetted length to get the characteristic length that…
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Ideal gas temperature calculator
One mole of gas at 101325 Pa filling 0.022414 m³ sits at about 273 K. Enter pressure in pascals, volume in cubic metres and the amount in moles; the gas…
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Ideal gas pressure calculator
One mole of gas at 298.15 K in 0.024465 m³ exerts about 101325 Pa, roughly one standard atmosphere.
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Ideal transformer calculator
A 240 V primary with 1000 turns and a turns ratio of 0.1 gives 24 V on a 100-turn secondary, a step-down transformer.
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Immersed weight calculator
A 50 N object displacing 0.002 m³ of water at 1000 kg/m³ reads 30.38 N on a scale, because the water pushes up with 19.62 N.
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Insertion loss calculator
Feed 1 W into a cable or filter, measure 0.5 W at the far end, and the insertion loss is 3.01029995664 dB.
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Internal resistance calculator
A 12 V battery that reads 11 V while delivering 2 A has an internal resistance of 0.5 Ω, with 1 V lost inside the cell.
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Intrinsic carrier concentration calculator
Textbook silicon values at 300 K, with densities of states of 2.8 × 10^25 and 1.04 × 10^25 per cubic metre and a 1.12 eV bandgap, give an intrinsic carrier…
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Knudsen number calculator
Sea-level air, whose molecules travel about 65 nm between collisions, flowing in a 1 mm channel gives a Knudsen number of 0.000065: plainly continuum flow.
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J-pole antenna calculator
At 146 MHz on the 2-metre band, a J-pole needs a 1.0266865 m half-wave radiator, a 0.51334325 m matching stub and a 1.54002975 m long element.
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Kepler third law
A satellite 42,164,000 m from the centre of Earth, whose mass is 5.9722 × 10^24 kg, takes 86163.3432753 seconds per orbit: one sidereal day.
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Laser spot size calculator
A 632.8 nm helium-neon beam 5 mm wide, focused by a lens with a 0.1 m focal length, comes to a spot 0.0000161141196782 m across.
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LED current calculator
A 5 V USB rail, a red LED with a 2 V drop and a 150 Ω resistor give 0.02 A through the diode, with 3 V across the resistor.
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Lensmaker's equation
Get the focal length of a thin lens from its material, the medium around it and its two curved faces: a lens of index 1.5 in air with radii of 0.1 and -0.1 m…
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Linear actuator force calculator
A motor torque of 1 N·m on a screw with a 5 mm lead at 0.9 efficiency pushes with more than 1000 N.
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Lorentz force calculator
A 2 C charge moving at 3 m/s along x, with a 4 V/m electric field along y and a 5 T magnetic field along z, feels 22 N along minus y.
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Lumen calculator
A 100 candela source shining into 2 steradians sends out 200 lumens. Enter the luminous intensity and the solid angle of the beam and get the luminous flux…
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Magnetic declination calculator
If a landmark lies at 50° true and your compass reads 45°, the local declination is 5° east. Enter both bearings of the same point and get the signed offset…
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Magnetic dipole moment calculator
A loop carrying 2 A around an area of 0.5 m² has a magnetic dipole moment of 1 A·m². Enter the current and the enclosed area of a single flat loop to get its…
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Magnetic force on a current-carrying wire
A wire carrying 2 A along 0.5 m of a 0.4 T field, at 90° to it, feels a force of 0.4 N. Enter current, length, field and the angle in degrees to get the force…
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Magnetic moment calculator
A 10-turn coil carrying 2 A around 0.05 m² has a magnetic moment of 1 A·m². Enter current, number of turns and loop area to get the moment of a whole coil, not…
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Magnitude of acceleration
Components of 3 and 4 m/s² along x and y give an acceleration of 5 m/s². Enter the axis components, leave the third empty for motion in a plane, and get the…
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Manometer calculator
A 0.2 m difference in a water column, at 1000 kg/m³ and 9.81 m/s², means 1962 Pa. Enter the column height difference, the liquid density and gravity to turn a…
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Mass to density calculator
An object of 12 kg that fills 3 m³ has a density of 4 kg/m³. Enter the mass you weighed and the volume you measured to get the density, with a clear refusal…
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🔬 ScienceFree
Maximum height projectile motion
A ball launched at 20 m/s and 45° under a gravity of 9.8 m/s² rises just over 10 m above its launch point.
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Mixed-air temperature calculator
Mixing 2 kg/s of air at 10 °C with 2 kg/s at 30 °C gives a blend at 20 °C. Enter the temperature and mass flow of each stream to get the adiabatic mixed-air…
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