Calculator Inputs
Formula Used
The Coriolis parameter quantifies how rotation deflects horizontal motion: f = 2 Ω sin(φ), where Ω is the planetary rotation rate (rad/s) and φ is latitude. The sign comes from sin(φ): positive in the Northern Hemisphere, negative in the Southern.
Two common advanced outputs are the inertial period T = 2π / |f| and the beta parameter (latitudinal gradient) β = df/dy = 2Ω cos(φ) / a, where a is planet radius.
How to Use This Calculator
- Select a planet preset, or choose Custom for your own Ω and radius.
- Enter latitude between −90° and +90°.
- Pick the output unit for f and optional advanced outputs.
- Press Calculate to see results above the form.
- Use the download buttons to export a report.
Example Data Table (Earth)
| Latitude (°) | f (s⁻¹) | Inertial period (hours) |
|---|---|---|
| 0 | 0 | — |
| 15 | 3.77468×10⁻⁵ | 46.24 |
| 30 | 7.29212×10⁻⁵ | 23.93 |
| 45 | 1.03126×10⁻⁴ | 16.92 |
| 60 | 1.26303×10⁻⁴ | 13.82 |
Values use Earth Ω ≈ 7.2921159×10⁻⁵ rad/s.
Professional Article (8 Headings)
1) What the Coriolis parameter represents
The Coriolis parameter, f, measures the rotational influence on horizontal motion in a rotating frame. It enters the momentum equations and sets how strongly trajectories turn for a given speed and length scale. In rotating-flow analysis, it is a first check for whether rotation will dominate the dynamics.
2) Latitude control and sign convention
This calculator uses f = 2Ω sin(φ). On Earth, Ω ≈ 7.2921159×10⁻⁵ rad/s. At 30°, f ≈ 7.29×10⁻⁵ s⁻¹; at 45°, f ≈ 1.03×10⁻⁴ s⁻¹. The sign flips across the equator with sin(φ), matching the hemispheric change in deflection direction.
3) Interpreting the magnitude |f|
|f| is central for time-scale estimates. Larger |f| supports geostrophic balance, where pressure-gradient forces and Coriolis effects nearly offset, producing along-isobar flow. When |f| is small, ageostrophic accelerations matter more and cross-isobar motion increases.
4) Inertial period as a measurable time scale
The inertial period T = 2π/|f| is the oscillation period of an ideal parcel with small friction. For Earth, typical values are 23.9 h at 30°, 16.9 h at 45°, and 13.8 h at 60°. These values help interpret drifter loops and near-inertial motions.
5) Why beta matters for waves and jets
The beta parameter β = df/dy = 2Ω cos(φ)/a captures how f changes with north–south distance. On Earth (radius a ≈ 6.371×10⁶ m), beta provides the restoring mechanism for Rossby waves, shapes jet meanders, and helps explain western boundary intensification in ocean basins.
6) Unit options and practical reporting
Equations typically use f in s⁻¹, while day⁻¹ can help quick comparisons over daily variability. Exports preserve your chosen f unit and record the inputs for traceable reports and notebooks. This supports consistent comparisons between locations, seasons, and experiments.
7) Using presets for other planets
Rotation rate and radius differ across planets, so f and β can change substantially at the same latitude. Presets speed up comparative checks, while Custom mode supports laboratory turntables or idealized parameter studies where you control Ω and radius directly.
8) Recommended workflow for consistent analysis
Select the body and latitude, compute f, |f|, and T, then enable β for wave or jet problems. For regional comparisons, evaluate several latitudes (for example 15°, 30°, 45°, and 60°). Export CSV or PDF so assumptions and results stay reproducible.
FAQs
1) Why is f zero at the equator?
Because sin(0°)=0, so f = 2Ω sin(φ) becomes zero. Near the equator, the Coriolis effect is weak and other balances or equatorial approximations become more relevant.
2) What does a negative f mean?
A negative value indicates Southern Hemisphere latitude, where sin(φ) is negative. The sign changes the direction of deflection; magnitudes such as |f| still set the time scale.
3) Which unit should I use for Ω?
Any provided unit is fine because the calculator converts to rad/s internally. Use rad/s for direct geophysical work, rev/day for rotation periods, or deg/hour if that matches your source data.
4) How accurate are the preset planet values?
They are representative constants suitable for educational and comparative calculations. For high-precision mission analysis, use Custom mode with the exact rotation rate and reference radius from your authoritative dataset.
5) What is the inertial period used for?
It estimates how quickly a parcel would rotate in an idealized inertial circle when friction is small. It helps interpret drifter tracks, current-meter records, and model outputs in rotating flows.
6) When should I care about beta?
Enable beta when studying Rossby waves, jet dynamics, or large-scale ocean circulation. Beta represents how f varies with latitude, which creates restoring forces and wave propagation characteristics.
7) Can I use this for lab turntable experiments?
Yes. Choose Custom, enter the turntable rotation rate, and set an effective radius for your setup if beta is needed. For uniform rotation experiments, you may focus on f and inertial period only.