Science
1,125 science calculators for chemistry, physics, biology, astronomy and the Earth sciences. Each one states the relation it uses and the units it expects, so class problems, lab work and quick checks come out right, free in your browser.
Reaction time calculator
At 20 m/s, a driver who needs 1.5 s to react covers 30 m before touching the brake. Enter speed and reaction time to get the thinking distance, the stretch of…
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Refrigerant capillary tube calculator
A 0.8 mm capillary carrying 1.5 kg/h of R134a needs a length of just under 3 m. Enter inner diameter, refrigerant and design mass flow to get a first-cut length…
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Relativistic kinetic energy calculator
At a tenth of the speed of light, the true kinetic energy is already a few percent above the classical ½mv².
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Resistor wattage calculator
A 100 Ω resistor carrying 0.05 A turns 0.25 W into heat, so it needs at least a 0.25 W rating. Enter resistance in ohms and current in amperes to get the…
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RLC circuit calculator
A series circuit of 10 Ω, 1 mH and 1 µF resonates at just over five thousand hertz, with a quality factor a little above 3.
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RLC impedance calculator
At 50 Hz, a series circuit of 100 Ω, 0.2 H and 10 µF is dominated by the capacitor, so its phase is negative and voltage lags current.
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RMS speed calculator
Quadruple the absolute temperature of a gas and the root-mean-square speed of its molecules doubles.
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Rotational stiffness calculator
A steel shaft with a shear modulus of 80 GPa, a polar moment of 1 × 10⁻⁸ m⁴ and a length of 0.5 m takes 1600 N·m to twist one radian.
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Rydberg equation calculator
An electron falling from level 3 to level 2 in hydrogen emits the Balmer H-alpha line at 656.112276418 nm in vacuum.
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Section modulus calculator
A section with I of 0.0001 m⁴ and its farthest fibre 0.05 m from the neutral axis has a section modulus of 0.002 m³.
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Shaft size calculator
A torque of 1000 N·m with an allowable shear of 40 000 000 Pa needs a solid shaft just over fifty millimetres across.
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Shear modulus calculator
A shear stress of 80 MPa that produces a shear strain of 0.001 means a shear modulus of 80 GPa, typical of structural steel.
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Shear wave velocity calculator
A solid with a shear modulus of 81 000 000 000 Pa and a density of 9000 kg/m³ carries shear waves at 3000 m/s.
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Simple harmonic motion calculator
With an amplitude of 4, an angular frequency of 2 rad/s and zero phase, the oscillator sits at +4 at time zero, at rest, with an acceleration of −16.
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Simple pendulum calculator
A 1 m pendulum under standard gravity, 9.80665 m/s², takes about 2 s for one full cycle. Enter the length from pivot to centre of mass and the local gravity to…
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Slenderness ratio calculator
A column with an effective length of 4000 mm and a least radius of gyration of 50 mm has a slenderness ratio of 80.
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Sound wavelength calculator
Concert A at 440 Hz in room air, where sound travels at 343 m/s, has a wavelength of about 0.78 m.
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Space travel time dilation
At 60% of light speed the Lorentz factor is 1.25, so clocks aboard run at 0.8 times the Earth rate.
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Specific gravity calculator
Aluminum at 2.7 g/cm³ against water at 1 g/cm³ has a specific gravity of 2.7, so it is denser than water.
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Speed of sound in solids
A steel bar with a Young's modulus of 2 × 10¹¹ Pa and a density of 8000 kg/m³ carries sound at 5000 m/s.
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Speeds and feeds calculator
A 10 mm end mill cutting at 100 m/min must turn at just over three thousand rpm. Add the number of teeth and the chip load per tooth and you also get the table…
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Spring calculator
A spring with a constant of 80 N/m stretched by 0.05 m pulls back with a force of −4 N, the minus sign pointing toward rest.
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Stefan-Boltzmann law
A black body with 1 m² of surface at 300 K radiates 459.300327939 W. Enter the area and the temperature in kelvin to get the total radiated power, with…
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Stokes' law calculator
A sphere of radius 0.0001 m and density 2500 kg/m³ settles at 0.0327 m/s through a liquid of 1000 kg/m³ and 0.001 Pa·s.
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Stopping distance calculator
At 20 m/s with a 1.5 s reaction time and 8 m/s² of braking, a car covers 30 m before braking starts and 25 m while braking, 55 m in all.
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Sunset time calculator
At the equator, with the Sun's declination at 23.44°, the Sun sets at 6 p.m. solar time, a 90° hour angle after noon.
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SUVAT calculator
Starting at 10 m/s with an acceleration of 2 m/s², a body reaches 20 m/s after 5 s. Enter the initial velocity, the acceleration and the time, then choose…
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Telescope field of view
A 50° eyepiece at 40× magnification shows 1.25° of real sky, enough for the full Moon with room to spare.
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Thermal energy calculator
Warming 2 kg of water by 10 °C, with a specific heat of 4184 J/(kg·K), takes 83680 J. Enter the mass, the specific heat and the temperature change to get the…
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Thermal expansion calculator
A 10 m steel member heated by 50 °C, with a coefficient of 0.000012 per kelvin, grows by 0.006 m to 10.006 m.
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Thermal resistance calculator
A 0.24 m wall with a conductivity of 0.8 W/(m·K) and a 15 m² face has a thermal resistance of 0.02 K/W.
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Thin lens equation
A converging lens with a 10 cm focal length and an object 30 cm away forms a real image 15 cm behind it.
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Thrust-to-weight calculator
Engines giving 760000 N of thrust on a vehicle weighing 380000 N make a thrust-to-weight ratio of 2, so it lifts off.
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Time dilation calculator
At 60% of light speed the Lorentz factor is 1.25, so one second on the moving clock lasts 1.25 seconds for the observer.
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Toilet paper race mass moment of inertia
A 0.2 kg roll with radii of 0.02 m and 0.05 m has a moment of inertia of 0.00029 kg·m² and an inertia factor of 0.58.
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Torsional spring calculator
A spring of 2 mm wire, 16 mm mean coil diameter, 8 active coils and E of 206000 N/mm² has a rate of 402.34375 N·mm per radian.
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Torsional stiffness calculator
A shaft with a shear modulus of 8 × 10¹⁰ Pa, a polar moment of 10⁻⁸ m⁴ and a length of 0.5 m resists twisting with 1600 N·m per radian.
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Transmission coefficient calculator
A wave going from a vacuum at 377 Ω into a medium of 150 Ω passes about eighty-one percent of its power and reflects the rest.
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True strain calculator
A 10% stretch, an engineering strain of 0.1, is a true strain of about 9.53%, and doubling a length gives about 0.693, not 1.
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Barrel twist rate calculator
A 0.308-inch bullet that is 1.2 inches long needs one turn every 11.858 inches of barrel, written 1:11.858, by Greenhill's formula.
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Valve flow coefficient calculator
Water flowing at 20 gallons per minute through a 4 psi drop needs a valve rated Cv 10. Enter the flow, the pressure drop and the specific gravity to get the…
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Velocity calculator
Divide the distance travelled by the time it took and get average velocity in metres per second: 100 m in 20 s is 5 m/s.
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Vickers hardness number calculator
Turn the test load and the mean impression diagonal into a Vickers hardness number: 10 kgf with a 0.2 mm diagonal gives about four hundred sixty-three HV, the…
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Voltage regulation calculator
Compare the voltage with the load disconnected against the voltage at full load and get regulation as a percentage: 220 V at no load and 200 V at full load mean…
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Volume to density calculator
Divide a sample's mass by the volume it occupies and get its density: 10 kg in 2 m³ gives 5 kg/m³, and grams over cubic centimetres give g/cm³.
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