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➗ MathFree
Compound rule of three calculator
If 8 workers in 6 days at 5 hours a day make 240 pieces, 12 workers in 4 days at 6 hours make 288: enter the known value and each quantity, direct or inverse…
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➗ MathFree
Collinear points checker
(0, 0), (1, 2) and (2, 4) lie on one line with slope 2: enter three points and see whether they are collinear, with the triangle area, the shared slope or a…
A
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➗ MathFree
Linear combination of two numbers
Find whole numbers to multiply 15 and 25 by so the sum is 10: 15 × 4 + 25 × (−2) = 10, possible because their greatest common divisor, 5, divides 10.
S
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➗ MathFree
Nested absolute value equation solver
||2x - 1| + 3| = 5 has two roots, -1/2 and 3/2: the solver peels the outer absolute value first, keeps only the inner value 2 because -8 is impossible, then…
S
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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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…
S
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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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…
S
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🔬 ScienceFree
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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🔬 ScienceFree
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.
B
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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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.
K
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🔬 ScienceFree
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…
K
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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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…
K
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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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…
K
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🔬 ScienceFree
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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🔬 ScienceFree
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…
K
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🔬 ScienceFree
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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🔬 ScienceFree
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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🔬 ScienceFree
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.
K
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🔬 ScienceFree
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…
B
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🔬 ScienceFree
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.
K
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🔬 ScienceFree
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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🔬 ScienceFree
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…
K
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📅 Dates & timeFree
Add minutes to a datetime
Add or subtract whole minutes from a date and time and get the result in UTC: 23:45:30 UTC on 25 July 2026 plus 30 minutes is 00:15:30 UTC on 26 July.
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📅 Dates & timeFree
Add quarters to a date
Move a date by whole quarters of three calendar months: 30 November 2024 plus 1 quarter is 28 February 2025, since February has no 30th.
K
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📅 Dates & timeFree
Date difference in years, months and days
From 31 January 2019 to 2 March 2024 is 5 years, 1 month and 2 days, or 1,857 days in total. Enter any two calendar dates to get the same calendar breakdown…
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📅 Dates & timeFree
Working days remaining in month
From July 20, 2026 to month end there are 9 working days left: 12 calendar days, minus 2 weekend days and 1 holiday on a weekday.
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📅 Dates & timeFree
Days remaining in the month
From 20 February 2024 there are 9 days left until the month ends on 29 February. Enter a date to get the days remaining, the last day of its month and the…
K
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📅 Dates & timeFree
Start and end of decade
13 August 2026 sits in the decade from 2020 to 2029, which opens on 1 January 2020 and closes on 31 December 2029.
K
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📅 Dates & timeFree
Fraction of year elapsed
At noon UTC on 2 July 2026 the year is exactly half over: the fraction is 0.5. Enter a date and time with Z or an offset such as +05:30 to see how far through…
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📅 Dates & timeFree
First and last day of year
For June 15, 2024, the year runs from 2024-01-01 to 2024-12-31 and has 366 days because it is a leap year.
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📅 Dates & timeFree
End of next month calculator
From 15 January 2024 the end of next month is 29 February 2024, because 2024 is a leap year. Enter any date and get the final day of the following month, ready…
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📅 Dates & timeFree
Nth weekday after a date
From Monday 18 March 2024, the first Monday after it is 25 March, not the same day, and the second is 1 April.
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📅 Dates & timeFree
Weekday of the first of the month from an ISO date
Enter any date and find the weekday on which its month began: 13 August 2026 gives 1 August 2026, a Saturday.
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📅 Dates & timeFree
Julian–Gregorian day offset calculator by date year
Enter a date and see the day gap between the Julian and Gregorian calendars for its year: in 2026 the Gregorian calendar is 13 days ahead.
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📅 Dates & timeFree
Week number within quarter
Enter a date to see which week of its calendar quarter it falls in: 20 May 2026 is in week 8 of Q2, counted from 1 April.
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📅 Dates & timeFree
Number of weeks in a month
August 2026 spans 6 calendar weeks when weeks start on Monday, because the month opens on a Saturday.
K
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📅 Dates & timeFree
Date to .NET ticks converter
29 February 2024 at 12:34:56.1234567 with a +02:30 offset is 638447978961234567 ticks, counted in UTC.
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📅 Dates & timeFree
Hebrew Year Length Calculator
Enter a Hebrew year number and get its exact length in days: 5784 has 383, a deficient leap year. You also see whether the year has a thirteenth month and how…
B
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📅 Dates & timeFree
Hijri month length calculator
Enter a Hijri year and month number and get its length: month 12 of 1446 AH has 29 days, because 1446 is not a leap year.
K
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📅 Dates & timeFree
Ethiopian to Gregorian date converter
Ethiopian New Year of 2016, month 1 day 1, is 12 September 2023 in the Gregorian calendar. Enter any Ethiopian year, month and day, including the five or six…
K
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1
Get your key
Create an account with your email and add balance when you need it. No subscription, no sales call.
2
Call the endpoint
One authenticated POST. The API returns a task_id immediately — copy-paste snippets in five languages on every page.
3
Collect the result
Receive a signed webhook the moment it's ready, or fetch a signed link. A failed task is never charged.
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The full API — 7800+ capabilities — billed only for what you run, from $0.002 per call. No monthly fee.
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