Advanced Coriolis parameter analysis for latitude and rotation. Track sign magnitude and inertial timing instantly. Clear outputs exports graphs examples formulas and practical guidance.
Use a preset planet or switch to custom rotation period or custom angular velocity. Results appear above this form after submission.
This graph shows how the Coriolis parameter changes with latitude for the currently selected rotation source.
The sample below uses Earth’s sidereal rotation rate and shows how the Coriolis parameter magnitude increases away from the equator.
| Latitude (deg) | sin(φ) | f = 2Ωsin(φ) (1/s) | Inertial period |
|---|---|---|---|
| 0 | 0.000000 | 0.00000000e+0 | Not defined at the equator |
| 15 | 0.258819 | 3.77467692e-5 | 1.927 days (46.238 h) |
| 30 | 0.500000 | 7.29211585e-5 | 23.934 h |
| 45 | 0.707107 | 1.03126091e-4 | 16.924 h |
| 60 | 0.866025 | 1.26303152e-4 | 13.819 h |
| 75 | 0.965926 | 1.40872861e-4 | 12.389 h |
f = 2Ωsin(φ)
Here, f is the Coriolis parameter, Ω is planetary angular velocity, and φ is latitude.
Ω = 2π / P
Use this when the spin period P is known in seconds. The calculator converts hours to seconds automatically.
Ti = 2π / |f|
This estimates the period of ideal inertial motion. It becomes undefined at the equator because f = 0.
β = 2Ωcos(φ) / R
The beta parameter shows how the Coriolis parameter changes with latitude on a sphere of radius R.
The Coriolis parameter, f, measures how strongly planetary rotation affects horizontal motion at a latitude. It equals twice angular velocity times the sine of latitude. Its sign changes across the equator, and its magnitude grows toward the poles.
At the equator, latitude is zero, so sin(0) equals zero. That makes f equal to zero, meaning the vertical component of planetary rotation does not produce the usual horizontal Coriolis deflection there.
Southern latitudes are negative, so sin(latitude) is negative. With positive planetary angular velocity, f becomes negative. That sign indicates the opposite rotational sense for large-scale deflection compared with the Northern Hemisphere.
The inertial period is the time a freely moving parcel takes to complete an ideal inertial circle. It equals 2π divided by |f|, so it becomes longer near the equator and shorter toward the poles.
Yes. The calculator accepts custom rotation period or angular velocity, plus planetary radius for beta. That lets you evaluate Earth, Mars, Jupiter, Venus, or any rotating world with known spin properties.
Beta is the latitudinal rate of change of the Coriolis parameter. In the spherical approximation, β = 2Ωcosφ / R. It matters in Rossby waves, geophysical fluid dynamics, and large-scale atmosphere or ocean dynamics.
Use the planet’s sidereal rotation period when you want the true spin rate relative to inertial space. Solar day values can differ because orbital motion changes the apparent noon-to-noon interval.
No. The calculator gives a precise local parameter, but real motion also depends on pressure gradients, friction, stratification, curvature, and geometry. Use it as a strong foundation for deeper physical analysis.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.