Earth science calculators
Choose the measurement you want to make. Each calculation starts with a populated example; change its inputs to compare your own geometry or observing location.
Earth curvature and hidden height
Separate tangent drop, horizon distance and hidden target height using eye height and an assumed refraction value.
Great-circle distance
Enter two latitude–longitude pairs to find their shortest spherical surface distance in kilometres and miles.
Sun position
Use a UTC date and observing location to find the Sun’s geometric altitude and compass bearing.
Earth radius from horizon dip
Use eye height and the angle below a level horizontal to infer the spherical radius. Enter the measurement uncertainties to see how strongly a small dip error changes the answer.
Eratosthenes shadow calculator
Compare signed noon zenith angles at two sites and their surface separation. The result gives circumference, radius and the contribution of independent distance and angle uncertainties.
Earth rotation speed calculator
Find the speed of a point carried around Earth’s axis at your latitude, then compare it with the equator. A latitude circle becomes smaller toward either pole.
Foucault pendulum calculator
Calculate the ideal turn of a pendulum’s swing plane at any latitude. Compare the signed hourly rate and full-turn period with the polar and equatorial cases.
Coriolis path calculator
Start with eastward motion in a horizontal rotating frame. Follow the path under the Coriolis term at one fixed latitude, with speed conserved throughout the track.
Angular size calculator
Compare a sphere’s apparent diameter with a flat circular disk of the same diameter at the same centre distance. Enter both lengths in the same unit.
Star trail rotation calculator
Plot one star’s changing sky direction during an exposure. Latitude places the celestial pole; declination sets the star’s distance from that pole.
Polaris altitude and latitude
Compare the north celestial pole’s altitude with Polaris’s upper and lower culminations. Enter the star’s declination for the observing date and your altitude-reading uncertainty.
Day length calculator
Compare the time the Sun is above the standard sunrise threshold at two latitudes on the same date. Results use a midnight-to-midnight UTC window and show each crossing in UTC.
Map projection distortion calculator
Compare one shortest spherical route on three maps, then inspect the local length and area distortion at your chosen latitude.
Horizon and lens projection
Plot the same geometric horizon through three camera projections. Change camera pitch and field of view to see how a misplaced horizon and a wide-angle lens alter the displayed line.
Atmospheric refraction ray calculator
Follow one launched ray through a lower layer and an upper layer. Compare its path with the same straight ray and a single constant gradient over the same spherical surface.
Three-site shadow model comparison
Enter three northward site distances and signed zenith angles on the same date. Fit one spherical curvature and one shared local-Sun geometry to the same observations.
Local Sun and globe sky comparison
Set three observing places and one UTC instant. Compare their solar directions with a nearby source moving on an explicitly defined north-polar plane.
Solar eclipse contact comparison
Compare the next local eclipse at two entered places. Start on 1 April 2024 to follow the North American eclipse; each table row gives its predicted UTC contact and Sun altitude.