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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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📅 Dates & timeFree
Subtract weeks from a date
Enter a date and a number of weeks to find the exact earlier day: 18 March 2024 minus 3 weeks, or 21 days, is 26 February 2024.
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🔬 ScienceFree
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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📅 Dates & timeFree
Add decades to a date
Move a date forward or back by whole decades, ten years each: 15 March 2024 plus 2 decades is 15 March 2044.
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📅 Dates & timeFree
Add hours to a datetime
Shift a date and time by a number of hours and read the result in UTC: 10:00 UTC on 1 March 2024 plus 5 hours is 15:00 UTC the same day.
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📅 Dates & timeFree
Difference in decades between dates
From 25 July 1985 to 25 July 2026, four whole decades have passed. Enter two calendar dates and get the number of completed ten-year periods between them…
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📅 Dates & timeFree
Difference in minutes between two datetimes
From midnight to half past one on 1 January 2024, both in UTC, 90 minutes pass. Enter two dates with times, with an offset such as +02:00 or a Z, and get the…
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📅 Dates & timeFree
Subtract minutes from a datetime
Move a date and time back by any number of minutes and get one clean UTC value: 00:15:30 on 1 January 2026 at UTC+2, minus 90.5 minutes, is 20:45:00 UTC on 31…
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📅 Dates & timeFree
Days remaining in the quarter
From 15 February 2026 there are 45 days left in the first quarter, counting that day and 31 March.
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📅 Dates & timeFree
Midpoint between two dates
Give two dates or times and get the exact instant halfway between them, in UTC: from midnight on 2024-01-01 to midnight on 2024-01-02, the midpoint is noon on…
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📅 Dates & timeFree
Nearest weekday to a date
Type a date and get the closest Monday-to-Friday business day: a Saturday becomes the Friday before, a Sunday the Monday after, and weekdays stay unchanged.
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📅 Dates & timeFree
Net working days between dates
From 1 to 10 July 2026 there are 7 working days once the weekend and a holiday on the 3rd are taken out.
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📅 Dates & timeFree
Working days in a year
2024 has 260 working days once New Year's Day and Christmas are removed: 366 days minus 104 weekend days and 2 weekday holidays.
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📅 Dates & timeFree
Business days until a date
From Friday 3 July to Friday 10 July 2026, 4 business days remain when Monday 6 July is a holiday.
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📅 Dates & timeFree
Start and end of century
15 June 2024 sits in the 21st century, which runs from 1 January 2001 to 31 December 2100. Enter any date to get the century's number, its first and last year…
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📅 Dates & timeFree
Fraction of quarter elapsed
At noon UTC on 15 February 2024 the first quarter is exactly half over: a fraction of 0.5. Enter a date, or a date and time with its offset, to see how much of…
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