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.
Moles to particles calculator
One mole of any substance is exactly 6.02214076 × 10²³ particles, so the calculator multiplies your moles by that constant and returns the count of atoms…
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Tonicity osmolarity ratio calculator
Normal saline at 308 mOsm/L against a 300 mOsm/L plasma reference gives a ratio of about 1.027, inside the isotonic band.
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Trouton's rule calculator
Water boiling at 373.15 K gives a Trouton estimate of 32837.2 J/mol for its enthalpy of vaporization.
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Acceleration due to gravity calculator
At 10 km, around a long-haul cruising altitude, gravity is about 0.3 % weaker than the standard 9.80665 m/s² at sea level.
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Acceleration of a charged particle in an electric field
A particle carrying 0.000002 C with a mass of 0.001 kg in a 5000 N/C field accelerates at 10 m/s².
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Acceleration calculator
A force of 20 N on a 5 kg mass gives an acceleration of 4 m/s². Enter the net force in newtons and the mass in kilograms; a negative force returns a negative…
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Acoustic impedance calculator
Air at 1.204 kg/m³, with sound at 343 m/s, has an acoustic impedance of 412.972 Rayl. Enter a medium's density and speed of sound to get the figure that decides…
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Air density calculator
At 1013.25 hPa, 15 °C and 60 % relative humidity, air weighs 1.220312 kg per cubic metre, a little less than the textbook 1.225 for dry air.
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Air pressure at altitude calculator
At 1,500 m the standard atmosphere puts the air pressure at 845.562621 hPa, against 1013.25 hPa at sea level.
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Alfvén velocity calculator
A 0.00005 T field in a plasma of 1.67 × 10⁻¹³ kg/m³ gives an Alfvén velocity of 109145.751826 m/s, more than 100 km per second.
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Alien civilizations calculator
With 1.5 stars born per year, planets around every star, 0.4 habitable worlds each, life wherever possible, 0.1 for intelligence, 0.2 for communication and a…
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Temperature at altitude calculator
If it is 20 °C at sea level, expect about 10.25 °C at 1,500 m, since the standard atmosphere loses 6.5 °C every 1,000 m.
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Amp to wire size calculator
A 20 A load on a 30 ft run at 12 V, allowing a 3 % drop, needs 4 AWG copper. Enter current, one-way length, voltage and drop budget to get the smallest gauge…
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Angle of incidence calculator
A ray going from index 1 into glass of index 1.5 at 30° continues at 19.4712206345° from the normal.
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Angle of refraction calculator
Going from index 1 into glass of 1.5 at 30°, a ray refracts to 19.4712206345° and turns by 10.5287793655°.
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Angle of twist calculator
A 100 N·m torque on a steel shaft 1.5 m long and 0.02 m across twists it 0.120877171969 rad, almost 7°.
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Angular frequency calculator
50 Hz mains corresponds to an angular frequency of 314.159265359 rad/s, with a period of 0.02 s. Enter any positive frequency in hertz to get ω in radians per…
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Angular resolution calculator
A 200 mm telescope observing green light at 550 nm can separate two stars 0.692018 arcseconds apart, its diffraction limit.
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Aperture area calculator
A 200 mm telescope mirror has a collecting area of 31415.926536 mm², four times that of a 100 mm mirror.
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API gravity calculator
A crude with a specific gravity of 0.85 reads 34.970588235294 degrees on the American Petroleum Institute scale and is classed as light.
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Arrow speed calculator
A 50 lb bow drawn 28 inches can launch a 400-grain arrow at up to 362.38 ft/s, the theoretical ceiling with perfect efficiency.
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Attenuation in dB
Going from 100 W in to 1 W out is a loss of exactly 20 dB, and halving the power costs about 3 dB.
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Ballistic coefficient calculator
A body with twice the ballistic coefficient slows half as fast in the same air. Enter mass, drag coefficient and cross-sectional area to get that number, plus…
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Bank angle calculator
At 120 m/s on a 1,500 m radius, a level turn needs a bank of just under 45°. Enter airspeed and radius in coherent units and read the angle in degrees and…
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Barn-pole paradox calculator
A 20 m pole moving at 0.9 times light speed shrinks to under 9 m in the frame of a 10 m barn, so it fits.
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Belt length calculator
Pulleys of 200 and 100 mm with shafts 500 mm apart need 1,000 mm of straight belt plus two wrap arcs and a 5 mm correction.
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Bend allowance calculator
A 90° bend at 5 mm inside radius in 2 mm sheet, with a K-factor of 0.33, takes just under 9 mm of arc.
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Binoculars range calculator
Under ideal conditions, 10x42 binoculars still resolve a 1.8 m person at more than 60 km, because the eye's limit, not the lens, sets the bound.
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Biot number calculator
With h of 25, a characteristic length of 0.05 m and k of 15, the Biot number is 0.083. Get that dimensionless number plus a check of whether a…
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Estimate the moon phase for any calendar date
April 8, 2024 comes out as a new moon, about 1 % lit and 28.59 days into the cycle. Enter any date to get the phase name, the lunar age, how much of the Moon is…
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Compost Carbon-to-Nitrogen Ratio Calculator
Three buckets of dry leaves at 60:1, one of cardboard at 350:1, two of grass clippings at 17:1 and one of kitchen scraps at 20:1 land above the 25:1 to 30:1…
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Estimate solar panels needed for your energy usage
A home using 30 kWh a day with panels that each make 1.8 kWh needs 17 panels, since 16 would give only 28.8 kWh.
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Aphelion distance from eccentricity calculator
An orbit with a semi-major axis of 10 and an eccentricity of 0.2 reaches an aphelion of 12, in the same unit.
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Orbital speed at altitude calculator
Find the speed needed to stay in a circular orbit at a set height: 400,000 m above Earth's 6,371,000 m radius takes 7,672.598648 m/s.
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Perihelion velocity calculator
Around the Sun, an orbit with a semi-major axis of 149597870700 m and eccentricity 0.0167086 reaches its closest point at 147098299718 m, moving at…
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Specific orbital energy from semi-major axis calculator
Get the energy per kilogram of a two-body orbit from its size alone: a semi-major axis of 7000000 m around Earth, with μ of 398600441800000, gives…
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Apparent magnitude from absolute magnitude and distance calculator
An object of absolute magnitude 4.83 at 10 parsecs appears at magnitude 4.83, because the distance modulus there is zero.
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Apsis speed ratio calculator
An orbit with eccentricity 0.5 is three times faster at periapsis than at apoapsis, while a circular orbit gives 1.
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Combined maneuver Δv calculator
Going from 7.8 to 7.5 km/s while turning the orbit 30° takes 3.970519835 km/s in a single combined burn.
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Escape burn delta-v calculator from a circular orbit
From a circular Earth orbit with a radius of 6,771 km, escaping takes a prograde burn of 3178.094418806551 m/s, not the full escape speed.
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Escape velocity at altitude calculator
At 400,000 metres above Earth's surface, escape velocity is 10850.5399996432 m/s. Enter the body's mass, its radius and the altitude to get the ideal escape…
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Orbital flight path angle calculator
On an orbit with eccentricity 0.5, the flight path angle at a true anomaly of 60° is 19.106605350869°, so the object is moving outward after periapsis.
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Hohmann Total Delta-V Calculator for Circular Orbits
A Hohmann transfer from a 7000000 m orbit to 42164000 m around Earth needs a total delta-v of 3770.7272333041296 m/s in two burns.
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Hohmann transfer orbit semi-major axis calculator
A Hohmann transfer from a radius of 7,000 km to 42,164 km follows an ellipse with a semi-major axis of 24,582 km, the average of the two.
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Hyperbolic semi-major axis calculator
For Earth, a flyby with an excess speed of 3 km/s follows a hyperbola with a semi-major axis of −44288.9379778 km.
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Gravity balance point distance calculator between two masses
Find the spot on the line between two masses where their pulls cancel out: for Earth and the Moon, 384,400,000 m apart, it sits about nine tenths of the way…
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L4 and L5 Lagrange Point Geometry Calculator
Place the two triangular Lagrange points from a single distance: with the bodies 2 units apart, L4 and L5 sit halfway along the line and form an equilateral…
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Brightness ratio to magnitude difference calculator
A source 100 times brighter than another sits 5 magnitudes lower: a ratio of 100 gives a difference of -5.
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Rocket final mass calculator
A 100000 kg rocket that gains 9400 of velocity with an exhaust velocity of 3500 ends with 6817.248197125795 kg and burns 93182.7518028742 kg of propellant.
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Orbital semi-latus rectum calculator
An orbit with a semi-major axis of 7000 and eccentricity 0.05 has a semi-latus rectum of 6982.5, in the same unit as the axis.
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Sphere of influence calculator
Find how far a moon or planet's own gravity dominates: the Moon, 384400 km from Earth, has a sphere of influence of 66170.0117012 km under the classic…
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Rocket structural coefficient calculator
See how much of a stage's mass is dry hardware: 1200 kg of structure and 8800 kg of propellant make 10000 kg, a structural coefficient of 0.12, with the cargo…
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Rocket thrust from mass flow
Multiply how much propellant leaves each second by how fast it leaves to get thrust: 100 kg/s at 3000 m/s gives 300000 N, the ideal figure for engine sizing and…
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Rocket thrust-to-weight ratio calculator
Compare engine thrust with the vehicle's weight at one moment: 7600000 N against 549054 kg under 9.80665 m/s² gives a thrust-to-weight ratio of…
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Differential tidal force calculator
Measure how strongly gravity stretches an object: the Moon, 384400000 m away, pulls the near and far sides of Earth apart by 0.00000219855615754 m/s², and…
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True anomaly from eccentric anomaly calculator
Turn the eccentric anomaly into the real angle of a body around its focus: with an eccentricity of 0.5, an eccentric anomaly of 90° becomes a true anomaly of…
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Blackbody radiant exitance calculator
Double a surface's absolute temperature and it radiates sixteen times more power per square metre; triple it and the figure rises eighty-one times.
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Bolometric magnitude calculator
A visual magnitude of 4.83 with a bolometric correction of -0.07 gives a bolometric magnitude of 4.76.
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Atmospheric extinction magnitude calculator
With an extinction coefficient of 0.2 magnitudes per airmass, a star seen through 1.5 airmasses loses 0.3 magnitudes to Earth's atmosphere.
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Mass ratio from barycenter calculator
Read the mass ratio of two orbiting bodies straight from their distances to the shared centre of mass: distances of 1,500,000,000 and 450,000,000,000 give a…
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