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.
WBGT estimate from temperature and humidity calculator
At 32 °C and 65% relative humidity in the shade, the estimated wet bulb globe temperature is just over twenty-eight degrees Celsius.
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Old wind chill calculator
A 10 m/s wind on air at 10 °C gives a Siple–Passel cooling power of about seven hundred thirty-eight kilocalories per square metre per hour.
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Wind direction to 32-point compass calculator
A wind direction of 73.2° becomes East by north, written EbN, point number 7 when North is 0, with its sector centered on 78.75°.
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Circular orbit speed calculator
With Earth's gravitational parameter of 398600441800000 m³/s² and a radius of 6778000 m, a circular orbit needs a little under 8 km/s.
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Orbital radius from vis-viva calculator
Find where on its orbit a spacecraft must be at a given speed, for example 7668.6356752 m/s on an orbit with a semi-major axis of 6778000 m around Earth, which…
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Semi-major axis from apsides
Average the farthest and nearest points of an orbit to get its size: an apoapsis of 7350 km and a periapsis of 6650 km give a semi-major axis of 7000 km, with…
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Orbital mean motion calculator
Find the average angle an orbiting body sweeps each second: with a gravitational parameter of 1 and a semi-major axis of 1, it advances 1 radian per second and…
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Semi-major axis from period calculator
Turn an orbital period into orbit size with Kepler's third law: with μ = 1 and a period of 2π the semi-major axis comes out as exactly 1, a quick check for…
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Orbital period with both masses
Get the real orbital period of two bodies that pull on each other: the Sun and Earth, 149,597,870,700 m apart, give about 365.25 days, because both masses…
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Characteristic energy C3 calculator
A hyperbolic excess speed of 3 km/s means a characteristic energy C3 of 9 km²/s², since C3 is that speed squared.
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Radial/transverse orbital velocity
Eccentricity 0.2, true anomaly 90°, angular momentum 60000 and gravitational parameter 398600 give a radial speed of 1.32866666667 and a transverse speed of…
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Hohmann second burn Δv calculator
Circularising at geostationary distance after a Hohmann transfer from a 6778000 m orbit around Earth takes a second burn of 1456.50088963 m/s.
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Launch window phase angle calculator for Hohmann transfers
Know when to launch: with a 258.9-day transfer to a planet that orbits in 686.98 days, the target must lead the departure planet by about 44 degrees at liftoff.
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Magnitude Difference to Brightness Ratio Calculator
Translate a magnitude difference into plain brightness: a gap of 5 magnitudes means the brighter star looks about 100 times brighter.
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Two-body reduced mass calculator
Earth at 5.972e+24 kg and the Moon at 7.342e+22 kg have a reduced mass of 7.252833384611822e+22 kg and a total of 6.04542e+24 kg.
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Rigid body Roche limit calculator
A primary of radius 6371 with density 5514 and a satellite of density 3340 give a rigid Roche limit of 9487.49547681 in the same unit, or 1.48916896512 primary…
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Total magnitude of equal stars calculator
One hundred stars of magnitude 5 seen together shine at magnitude 0, exactly five magnitudes brighter than one of them.
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Radial Velocity from Doppler Shift Calculator
A line observed at 656.5 nm instead of its rest value of 656.28 nm means the source is receding at 100.49725842629394 km/s.
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White dwarf radius from mass calculator
See how a white dwarf shrinks as it gains mass: a star of 0.6 solar masses comes out at 8658067.050113482 m in radius, and the size falls to zero at the 1.44…
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Wien peak wavelength calculator
Turn a blackbody temperature in kelvins into the wavelength where its glow peaks: 5778 K gives about half a micrometre.
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CMB Temperature at Redshift Calculator
At redshift 3 the cosmic microwave background was four times hotter than today: 10.902 K instead of 2.7255 K.
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Critical density of the universe calculator
With a Hubble constant of 70 km/s per megaparsec, the critical density of the universe is 9.203873922972522 × 10⁻²⁷ kg per cubic metre.
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Photon Flux from Luminosity Calculator
A 1 watt source at 500 nanometres emits 2517058283771354600 photons every second. Enter the power and wavelength of any single-wavelength source, from a star to…
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Central mass from moon orbit calculator
A moon's period and orbit size reveal the mass of the planet it circles, and a 1 % error in the orbit's size shifts the result by about 3 %.
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Hubble constant from velocity and distance calculator
A galaxy receding at 7,000 km/s at a distance of 100 Mpc gives a Hubble constant of 70 km/s/Mpc. Enter one galaxy's recession velocity and distance to get H0 =…
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Focal ratio and f-number calculator from focal length and aperture
A telescope with a focal length of 1,200 mm and an aperture of 200 mm has a focal ratio of 6, written f/6.
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Seasonal Solar Declination Range Calculator
An Earth-like tilt of 23.4393 degrees means the star stands directly overhead somewhere between -23.4393 and +23.4393 degrees of latitude over the year.
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Planet orbital speed around a star calculator
With the Sun's mass of 1.98847e+30 kg and Earth's mean distance of 149597870700 m, a planet circles at 29785.1421692 m/s.
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True field of view calculator
Check whether a target fits in one view before you observe: an eyepiece with a 50° apparent field at 100x shows a true field of 0.5°, roughly the width of the…
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Julian Date to Gregorian date and time calculator
Julian Date 2451545 is 1 January 2000 at 12:00:00, because each whole Julian Date starts at noon. Enter one number and get the year, month, day, hours, minutes…
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Pixel Sampling and Resolution Check Calculator
Pixels of 3.76 µm behind 800 mm of focal length give 0.969445 arcseconds per pixel, so 2.2 arcseconds of seeing spreads over 2.269339 pixels: well-sampled.
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Star trail length calculator
Know the length of a star trail before you press the shutter: a 120-second exposure of a star at 30° declination draws a trail of 0.434198251573°, and a star at…
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Azimuth from equatorial coordinates calculator
A star at declination 20° and hour angle 45°, seen from latitude 52°, sits between south (180°) and west (270°).
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Day of year calculator from a calendar date
December 31, 2024 is day 366 of its year, because 2024 is a leap year. Enter a date as year-month-day and get its position in the year, counting January 1 as…
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Equation of time approximation calculator
On day 81 of the year the equation of time is −7.53 minutes, so a sundial reads earlier than a mean-time clock.
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Orbital radius from period in days calculator
Turn an orbital period in days into the orbit's size in astronomical units: 365.25 days around one solar mass gives exactly 1 AU.
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Black hole evaporation time calculator
Double a black hole's mass and its Hawking evaporation time grows eight times, because lifetime scales with the cube of mass.
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Orbital altitude from period and body calculator
Find how high a satellite flies from how long one lap takes: a period of 5400 seconds around Earth puts the orbit about two hundred eighty kilometres above the…
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Orbital speed in kilometres per second calculator
A body of 1 solar mass orbited at 1 astronomical unit gives a circular speed of 29.7851421692 km/s, the Earth-like case.
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Reflected-Light Planet Apparent Magnitude Calculator
A planet 71492 km in radius with albedo 0.538, 5.2 AU from the Sun and 4.2 AU from you, shines at magnitude -2.767353.
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Stellar luminosity in solar units calculator
Compare a star's power output with the Sun's from two ratios: twice the Sun's radius and 1.5 times its temperature give 20.25 solar luminosities, because…
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Frequency from angular frequency calculator
Turn radians per second into hertz without mixing the two up: about 6.283185 rad/s is one full cycle each second, so 1 Hz, and the result keeps your original…
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Transverse wave maximum particle acceleration calculator
A wave with a 0.02 m amplitude and an angular frequency of 10 rad/s gives each particle a peak acceleration of 2 m/s².
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Closed pipe harmonic frequency calculator
Finds the resonances a closed-open pipe actually supports: the third harmonic of a 0.5 m pipe with sound at 343 m/s is 514.5 Hz.
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Standing Wave Nodes Count Calculator for Fixed Ends
The fourth harmonic of a string fixed at both ends has 5 nodes: the two ends plus 3 interior points that never move.
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Wave Power Transmittance Calculator from Impedances
See how much wave power gets through an impedance mismatch: going from 50 to 75 gives a transmittance of 0.96, so nearly all the power continues.
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Wavelength from frequency and wave speed calculator
Divide the speed by the frequency and you have the length of one cycle: a 500 Hz sound moving at 340 m/s has a wavelength of 0.68 m.
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Sound intensity level calculator
An intensity of 1 × 10^-6 W/m² against the 1 × 10^-12 W/m² hearing threshold is 60 dB, a ratio of one million.
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Sound Power from Intensity and Area Calculator
An average intensity of 0.0025 W/m² across 12 m² carries 0.03 W of sound power. Use it for a test surface, an opening or a panel, and see the substitution…
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Speed of sound in solid calculator
With a Young modulus of 200 GPa and a density of 7850 kg/m³, the calculator gives the speed at which a longitudinal wave runs along a thin rod, in m/s and km/h.
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String harmonic series list calculator from fundamental frequency
A string with a 110 Hz fundamental has harmonics at 220, 330, 440, 550 and 660 Hz. Enter the fundamental and how many harmonics you want, and get the numbered…
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Acoustic pressure from intensity calculator
Gives the RMS pressure behind a measured sound intensity, so 0.001 W/m² in air at 1.225 kg/m³ and 343 m/s is just under two-thirds of a pascal.
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Sabine Reverberation Time Calculator
A 150 m³ room with 30 metric sabins of absorption has an RT60 of 0.805 s. Compare treatment options quickly: doubling the absorption halves the reverberation…
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Frequency to MIDI note number calculator
Find which MIDI key a measured pitch belongs to: 440 Hz is note 69 (A4) with zero cents off, and any other frequency shows its nearest note plus how far it sits…
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Room Volume from Reverberation Time Calculator
A room with an RT60 of 1.2 s and 50 metric sabins of absorption implies a volume of 372.670807453 m³.
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Equal temperament note frequency calculator
Turn a reference pitch and a number of semitones into a frequency: 440 Hz moved up 12 semitones is 880 Hz, one octave higher, and every step multiplies by the…
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Thin lens image distance calculator
Know where to put the screen: a lens with a focal length of 10 and an object 30 away forms a real, inverted image 15 away, in whatever length unit you used for…
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Telescope exit pupil calculator
A 200 mm telescope working at 100x has a 2 mm exit pupil, the disk of light that enters your eye. Enter the aperture and the magnification to compare eyepieces…
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Thick lens focal length calculator
Index 1.5, radii of 0.1 m and −0.1 m and a 0.01 m centre thickness give a converging lens with an effective focal length of 0.101694915254237 m.
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Two-lens system image position calculator
With focal lengths of 0.1 m and 0.2 m, lenses 0.5 m apart and an object 0.3 m away, the first image sits at 0.15 m and the final image is real and upright.
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