Calculator
Example data table
| Scenario | Distance | Time | Bearing | Computed speed |
|---|---|---|---|---|
| Continental margin drift | 120 km | 3 Myr | — | 40 km/Myr (≈ 40 mm/yr) |
| GPS baseline change | 18 mm | 1 yr | 65° | 18 mm/yr with components |
| Angular plate rotation | — | — | — | v = ω·r at chosen radius |
Formula used
v = d / tVn = v · cos(θ) Ve = v · sin(θ)v = ω · rv = d/t, the relative uncertainty is:σv / v = √[(σd/d)² + (σt/t)²]v = ω·r and s = v·t.How to use this calculator
- Select a mode that matches your measured quantities.
- Enter values and units. Use consistent uncertainty units if added.
- Click Calculate. Results appear above the form, below the header.
- Review outputs in mm/yr, m/s, and km/Myr as needed.
- Export CSV for spreadsheets or PDF for printing and sharing.
1) Why plate motion numbers matter
Plate motion rates help translate maps and seismic observations into measurable kinematics. A few millimeters per year can reshape basins over millions of years, while faster plates drive frequent deformation at boundaries. This calculator turns field distances, GPS baselines, or angular rotation rates into comparable velocity units for analysis.
2) Typical velocity ranges seen worldwide
Most modern plates move on the order of 5–100 mm/yr. Fast oceanic plates can approach the high end, while stable continental interiors often show smaller relative rates. Converting units is useful: 1 mm/yr equals 1 km/Myr, so a 40 mm/yr drift corresponds to about 40 km over a million years.
3) Distance–time estimates for geologic markers
When you have an offset marker such as a displaced river channel, dated lava flow, or mapped ridge segment, the speed estimate follows v=d/t. Use consistent distance and time units, then compare results in mm/yr or km/Myr. The example table reflects common teaching-scale values used in labs and exercises.
4) Bearings and vector components
Motion is often directional, especially when comparing stations across a fault zone. If you provide a bearing measured clockwise from north, the calculator resolves the speed into north and east components using Vn=v·cosθ and Ve=v·sinθ. Components support plotting vectors on maps and combining motions.
5) Angular rotation and surface speed
Some plate models express motion as an angular velocity around an Euler pole. The surface speed at a radius r is v=ω·r after converting ω to radians per second. The built‑in Earth mean radius is 6371 km, a standard approximation for global-scale kinematics.
6) Uncertainty and data quality
Real measurements carry uncertainty from dating, mapping, or instrument precision. When you enter both uncertainty terms, the calculator applies standard relative-error propagation. For v=d/t, the fractional uncertainty is σv/v=√[(σd/d)²+(σt/t)²]. This produces defensible ranges for reporting and comparison.
7) Using consistent time scales
Plate motions are commonly reported in mm/yr, but geologic ages may be in kyr or Myr. Conversions can shift interpretation dramatically if mixed. This tool uses 365.25 days per year to keep time conversions consistent with common geoscience practice, helping you compare GPS-era and geologic-era estimates fairly.
8) Practical reporting and exporting
For workflow speed, export results directly. CSV is convenient for spreadsheets and plotting packages, while PDF provides a clean one-page report for lab submissions, field notes, or project documentation. Keeping inputs and outputs together reduces transcription errors and preserves assumptions like units, bearings, and uncertainty choices.
1) What is a reasonable plate speed for a quick check?
Many relative plate motions fall between 5 and 100 mm/yr. If your result is far outside that range, re-check units, time scale, and whether the distance represents total offset or only one component.
2) Why does the calculator show mm/yr and km/Myr?
They are equivalent scales used in different contexts. Because 1 mm/yr equals 1 km/Myr, you can switch between modern GPS reporting and million‑year geologic interpretations without changing the physical meaning.
3) How should I measure the bearing angle?
Use degrees clockwise from geographic north. For example, 90° points east and 180° points south. This convention matches common mapping practice and makes the north and east component outputs easy to interpret.
4) When should I use angular rate mode?
Use it when motion is given as an angular velocity about an Euler pole or rotation axis. The tool converts ω to radians per second and returns the corresponding surface speed at your chosen radius.
5) Do I need to enter uncertainties?
No. Uncertainty is optional and only computed when both relevant uncertainty fields are filled. Entering uncertainties is recommended when results will be compared across studies or reported in lab work.
6) Why use 365.25 days per year?
It approximates the mean solar year and is widely used for long-term geoscience conversions. Using a consistent convention helps keep mm/yr and Myr-based comparisons coherent across datasets.
7) What should I export for a report?
Export CSV for plotting and further calculations, and export PDF for a clean, print-ready summary. Both exports include the input values and the key results to support reproducibility.