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.
Proper motion calculator
A star moving sideways at 20 km/s at a distance of 10 parsecs drifts 0.42194092827 arcseconds per year across the sky.
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Surface brightness calculator
Spread a galaxy's total light over its patch of sky: a magnitude of 10.5 across 120 square arcseconds gives a mean surface brightness of 15.697953 mag/arcsec²…
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Combined magnitude of two stars
A magnitude 1 star and a magnitude 2 star seen as one point shine at magnitude 0.6361488422, brighter than either alone.
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Planet equilibrium temperature calculator
A planet receiving 1,361 watts per square metre with a Bond albedo of 0.3 balances at 254.578140117 K.
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Main-sequence lifetime calculator
Estimate how long a star burns hydrogen in its core: the Sun gets 10 billion years, while a star of two solar masses lives less than two billion.
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Stellar lifetime energy calculator
Multiply a star's luminosity by how long it shines to get the energy it radiates: 3.828 × 10²⁶ W for 3.15576 × 10¹⁷ seconds gives 1.208024928 × 10⁴⁴ joules…
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Stellar flux at planet calculator
Spread a star's power over a sphere to see what reaches a planet: 3.828 × 10²⁶ W at 149597870700 m gives 1361.1664654085753 W/m², and doubling the distance cuts…
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Chandrasekhar mass limit calculator
For a carbon-oxygen white dwarf, with a mean molecular weight per electron of 2, the Chandrasekhar limit is 1.4575 solar masses.
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Hubble time calculator
With a Hubble constant of 70 km/s/Mpc, the Hubble time is 13.9684603097 billion years, the reciprocal of today's expansion rate.
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Simple lookback time calculator
Estimate how long ago the light from a nearby galaxy set off: a redshift of 0.05 with a Hubble time of 14 billion years gives about 700 million years.
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Matter density at redshift calculator
See how dense matter was when the universe was smaller: at a redshift of 2 it was 27 times denser than today, so 2.7 × 10⁻²⁷ kg/m³ becomes 7.29 × 10⁻²⁶ kg/m³.
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Scale factor from redshift calculator
Light with a redshift of 3 left its source when the universe had a scale factor of 0.25, a quarter of its present size.
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Stellar angular diameter calculator
See how big a star looks from its size and how far away it is: the Sun, with a radius of 695700000 m seen from 149597870700 m, spans 1918.45545708 arcseconds…
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Stellar surface escape velocity calculator
Find the minimum speed needed to leave a star from its visible surface: the Sun, with 1.98847 × 10³⁰ kg and a radius of 695700000 m, gives 617684.0394130623…
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Universe age from Hubble constant
With a Hubble constant of 70 km/s/Mpc, the simple matter-only model gives an age of a little over 9 billion years, two-thirds of the Hubble time.
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Low-redshift luminosity distance calculator
Get the distance to a nearby galaxy or supernova from its redshift alone. A redshift of 0.01 with a Hubble constant of 70 gives 42.827494 megaparsecs.
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Planet mass from surface gravity
Recover a world's mass from how strongly it pulls at its surface: 9.82 m/s² with a radius of 6,371,000 m gives Earth's mass, about 5.97 × 10²⁴ kg.
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Moon orbital speed calculator
See how fast a moon circles its planet: with Earth's mass and a distance of 384,400,000 m, our Moon moves at just over one kilometre per second.
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Planet mass from density and radius calculator
A mean density of 5514 kg/m³ and a radius of 6371000 m give a mass of 5.972802939487484e+24 kg. Work out the mass of any round body from its density and size…
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Solar Day Length Calculator
Combine one spin relative to the stars with the length of the year to get the real noon-to-noon day: 23.9344696 hours of rotation and a year of 8765.8128 hours…
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Telescope light-gathering power calculator
See how many times more light your telescope gathers than your eye: a 100 mm objective against a 7 mm pupil collects about 204.08 times as much.
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Minimum useful magnification calculator for telescopes
Know the lowest power worth using: a 200 mm telescope with a 7 mm eye pupil needs at least 28.571429 times, or part of the light misses your eye.
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Moon illuminated fraction calculator
Find how much of the Moon's face is lit from the Sun–Moon–observer angle: at a phase angle of 90 degrees exactly half the disk shines, a quarter moon.
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Planet year length calculator
A star of 1.98847e+30 kg and an orbit of 149597870700 m give a year of 365.251375845 days, or 31557718.873 seconds.
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Rayleigh angular resolution calculator
Green light at 550 nanometres through a 100 mm aperture gives a Rayleigh limit of 1.3840368499180167 arcseconds.
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Solar declination by day of year
Type a day of the year and see how far north or south of the equator the Sun stands: day 172, near 21 June, gives 23.45°, using a smooth seasonal model.
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Airmass from altitude calculator
A target 30 degrees above the horizon has an airmass of 2, twice the air it would cross straight overhead.
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Aperture from focal ratio calculator
A 1200 mm telescope at f/6 has a 200 mm aperture: the focal length divided by the f-ratio. Enter both numbers from the tube or catalogue and get the diameter…
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Focal reducer calculator
A 2000 mm telescope at f/10 with a 0.63× reducer works at 1260 mm and f/6.3, while its 200 mm aperture stays the same.
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Image scale calculator
Turn a camera's pixel size and a telescope's focal length into arcseconds per pixel: a 3.76 µm pixel behind an 800 mm telescope covers just under one arcsecond…
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Modified Julian Date calculator
Turn a Julian Date into the shorter Modified Julian Date that satellite teams and astronomy archives use: JD 2451545 becomes MJD 51544.5 once 2400000.5 days are…
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Sidereal drift rate calculator
A star at 60° declination drifts through a stationary telescope at 7.5 arcseconds per second, half the equatorial rate, so you can time drift alignment…
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Days since J2000 epoch calculator
Julian Date 2451546.5 lies one and a half days after the J2000.0 epoch, and 2451544.0 lies one day before it.
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Declination from horizontal coords
An object due south at altitude 50°, seen from latitude 40°, has a declination of 0°: it sits on the celestial equator.
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Hour angle from LST and right ascension calculator
With Local Sidereal Time at 10.5 hours and a right ascension of 8.25 hours, the hour angle is 33.75°: the object has moved west of the meridian.
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Precession of declination calculator
At a right ascension of 0 degrees, a precession constant of 20.0431 arcseconds per year moves the declination by the full 20.0431 arcseconds each year.
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Right Ascension from Ecliptic Coordinates Calculator
Ecliptic longitude 139.686111°, latitude 4.875278° and obliquity 23.4392911° give a right ascension of 9.581501739524 hours.
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Transit altitude from declination calculator
Know the highest point an object reaches in your sky before you plan a night: at latitude 52°, a target at declination 20° transits 58° above the horizon, 32°…
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Black hole event horizon area calculator
A black hole of 1.9885 × 10³⁰ kg has a Schwarzschild radius of 2953.383939028493 metres and an event horizon area of 109609874.7781291 square metres.
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Orbital period in days calculator
Get an orbit's period in days straight from astronomical units and solar masses: 1 AU around one solar mass gives 365.25 days.
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Photon sphere radius calculator
A black hole of 1.98847e+30 kg, the mass of the Sun, has its photon sphere 4430.009073100317 m from the centre, one and a half times its event horizon radius of…
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Binary Roche lobe radius calculator
Two equal-mass stars 10 units apart each have a Roche lobe radius of 3.78920518380456 units, 0.378920518380456 of the separation.
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Hohmann departure speed calculator
Get the speed that starts a Hohmann transfer: leaving a 6678 km orbit for one at 42164 km around Earth, with μ of 398600.4418 km³/s², takes 10.1516085074 km/s…
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Bond albedo from reflected flux calculator
If 102 units of flux are reflected out of 340 that arrive, the Bond albedo is 0.3, meaning thirty percent of the energy goes back to space.
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Escape to circular speed ratio calculator
A circular orbital speed of 7800 m/s means an escape speed of 11030.865786510141 m/s at the same radius, because escape is always √2 times circular.
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J2 nodal precession rate calculator for satellite orbits
See how a planet's bulge slowly swings an orbit around: an orbit of 7000 km inclined 98 degrees above Earth has its ascending node advance about one degree per…
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Relativistic perihelion precession calculator
Mercury's orbit, with a semi-major axis of 57909050000 m and eccentricity 0.20563, advances 0.10351735428 arcseconds per orbit under general relativity.
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Exoplanet transit duration calculator
Know whether a whole transit fits in one night: a planet with a 3.5-day period orbiting at ten stellar radii crosses its star in 2.67827955606 hours, about…
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Orbit total energy calculator
Get the total energy of an orbit from its size alone: a 1000 kg craft on an orbit with a 7,000,000 m semi-major axis has -28,471,460,128.57143 joules, so it…
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Phase difference to path difference calculator
A phase shift of π/2 is a quarter cycle, so with 632.8 nm light the two waves differ by 158.2 nm of path.
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String wave average power calculator
A wave with 0.05 kg/m, 20 m/s, 10 rad/s and a 0.02 m amplitude carries 0.02 W along the string. Enter those four values for your own wave and see the average…
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Wave intensity inverse square law calculator
Move three times farther from a point source and the intensity drops to one ninth: 120 measured at 2 m becomes one ninth of that at 6 m.
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Angular wave number calculator
Go from wavelength to angular wave number in one step: 1 m gives 2π, or 6.28318530718 radians per metre.
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Wave phase value calculator
Find where a travelling wave sits in its cycle at a given place and instant: wave number 2, position 3, angular frequency 4, time 1 and starting phase 0.5 give…
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Closed pipe fundamental frequency calculator
Gives the lowest note of a closed-open air column: a 0.5 m pipe with sound at 343 m/s resonates at 171.5 Hz, with a wavelength of 2 m.
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Group velocity calculator
Turn two measured dispersion points into the speed of a pulse envelope: angular frequencies of 1e15 and 1.2e15 rad/s at wave numbers of 1e7 and 1.1e7 rad/m give…
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Shallow water wave speed calculator
Water 10 m deep carries a long wave at 9.90285312423 m/s under standard gravity. Enter the depth, and a local gravity if you need one, to estimate tides…
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Standing wave antinodes count calculator
The third harmonic of a string fixed at both ends has 3 antinodes, 4 nodes and 3 loops: enter any harmonic number and get the antinode count, which always…
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String linear density from frequency calculator
A string vibrating at 110 Hz over 0.65 m under 80 N has a linear density of 0.003912171744 kg/m. Enter the measured frequency, length and tension to find how…
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String nth harmonic frequency
On a 0.75 m string with a wave speed of 120 m/s, the third harmonic sounds at 240 Hz, three times the 80 Hz fundamental.
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