Plate Motion Rate Converter

Turn a distance and a time span into a plate motion rate, then look ahead.

Worked example — Plate Motion Rate Converter

Motion rate	3 cm/yr
Past	3000 km
Motion rate (mm/yr)	30 mm/yr
Projected future distance	1500 km

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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Lesson

The theory — Plate Motion Rate Converter

A plate motion rate is one division: a distance that two places have separated by, over the time it took. What makes it worth a page is not the arithmetic but the units — the answer is naturally in kilometres per million years, and geologists want centimetres per year.

What each symbol means

d: the separation in kilometres, usually inferred from matching features or from the age of the seafloor between them rather than measured directly.
T: the elapsed time in millions of years. Pairing a distance in kilometres with a time in millions of years is what makes the unit conversion below the interesting part.
rate: the speed, reported twice in two units. Both rows are the same division; the second exists because mm/yr is what a geodetic instrument reports and cm/yr is what a textbook quotes.

Where the formula comes from

The rate is d/T. For 3000 km over 100 million years that is 30 kilometres per million years.
Now convert, and do it by cancelling rather than by remembering: 1 km is 10⁶ mm and 1 million years is 10⁶ yr, so 1 km/Myr is 10⁶ mm / 10⁶ yr — exactly 1 mm/yr. The two powers of ten cancel completely.
So the rate in millimetres per year is the same number as the rate in kilometres per million years, and centimetres per year is that divided by ten. 30 km/Myr becomes 30 mm/yr and 3 cm/yr — which is why the two rate rows on this page always print figures ten apart.

How to read what you see

The pair of rate rows is the conversion made visible: 3 cm/yr beside 30 mm/yr, and the kilometres-per-million-years you would get by hand is that same 30. Try the other presets and the pattern holds — 6000 km over 120 million years gives 5 cm/yr and 50 mm/yr; 500 over 50 gives 1 cm/yr and 10 mm/yr. The projection row then simply multiplies: 3 cm/yr for another 50 million years is 1500 km.

Assumes: A rate that has held constant over the whole span, and that goes on holding for the projection. Both are conveniences rather than observations — spreading rates are known to have changed, sometimes sharply.
Breaks when: The projection is where the arithmetic outlives the geology. 500 km over 50 million years projected forward 100 million years gives 1000 km, and the number is arithmetically perfect and geologically fiction: it extrapolates twice as far as the evidence reaches, over a span in which plates demonstrably change direction, and it assumes an ocean can keep opening rather than beginning to close. A rate measured over a past interval is a description of that interval, not a property of the plate.

Plates move at the speed a fingernail grows 🖖

Typical plate motion is a few centimetres a year — the Atlantic widens by roughly 2.5 cm, about the rate your fingernails grow, which is why continental drift was dismissed for decades as unmeasurable. The numbers only become impressive when you multiply by geological time. At 2.5 cm a year a plate covers 25 km in a million years, and 2 500 km in a hundred million. India did better than that: it crossed roughly 6 000 km of ocean in about 50 million years, averaging some 12 cm a year, which is exceptionally fast for a continent. When that unusually quick plate hit Asia it had nowhere to go but up, and the Himalaya are what a fingernail-speed collision builds given enough time.

Practice

Check yourself

Predict the answer first, then use the controls above to find out. Reveal only after you have committed to a guess — that is what makes it practice.

Insight 1 says India crossed roughly 6000 km of ocean in about 50 million years. Enter those two numbers — and watch the sentence under the readout as you do.

Show answer

12 cm/yr and 120 mm/yr, and the commentary changes with them: the usual line about 1-10 cm/yr being typical is replaced by one warning that this is unusually fast and that even the fastest-spreading ridges rarely pass about 15-16 cm/yr. The page grades what you typed. India was nearly five times the Atlantic's 2.5 cm/yr, which is why that collision built the Himalaya instead of a gentle rise.
Enter the Atlantic's 2.5 cm/yr the long way round — 2500 km over 100 million years — then project forward 100 million years. Predict the projected distance before you look.

Show answer

2500 km: the number you typed in. That is not a coincidence, and it is worth seeing once — projecting forward for exactly as long as the measurement covered has to reproduce the measured distance, since both are the same rate over the same span. It also makes the assumption visible. The projection row is not evidence about the future; it is the past copied forward, and the further you drag it, the more of the answer is the copy.

Problem solved in full

An ocean 3000 km wide opened over 100 million years 5 steps
An ocean 3000 km wide, opened over 100 million years. Work out the spreading rate, and then check it against something you can see.
1. The rate is a division, and the whole difficulty is the units: kilometres over millions of years, converted to centimetres over years, is a factor of 10⁵ over a factor of 10⁶.
  
  $v = \frac{3000 km}{100 Myr} = \frac{3 \times 1 0 ^{8} cm}{1 0 ^{8} yr} = 3 cm/yr = 30 mm/yr$
2. Three centimetres a year. The reason this number is worth converting is that it is now comparable to something human — roughly the rate a fingernail grows.
3. Running it forward is the same arithmetic. Fifty million years at 3 cm/yr adds 1500 km.
  
  $d = v t = 3 cm/yr \times 50 \times 1 0^{6} yr = 1.5 \times 1 0^{8} cm = 1500 km$
4. Running it over a human lifetime instead gives 2.4 m — enough to be surveyed easily, and it is: plate motions are now measured directly by satellite geodesy rather than inferred from the rocks.
  
  $80 yr \times 3 cm/yr = 240 cm = 2.40 m$
5. And at this rate a plate would take 1.34 billion years to travel Earth's circumference, which is why continents have circled the globe only a handful of times.
  
  $\frac{40 075 km}{3 cm/yr} = 1.34 \times 1 0^{9} yr$
Answer

The tool prints 3 cm/yr, 30 mm/yr and 1500 km over the next 50 million years. The comparison to keep is the fingernail: geology's timescales are unimaginable but its speeds are not, and this one is slow enough that nothing in a human life looks like it is moving, yet fast enough to open an ocean since the dinosaurs. Both statements come from the same 3 cm/yr. At this rate the 5000-odd km of Atlantic seafloor takes on the order of 175 million years to produce, which is the same order as the age geologists assign to its opening — a consistency check you have just done from two numbers and a division.

$v = 3 cm/yr : 1500 km in 50 Myr, 2.4 m in a lifetime$

References (2)

The current plate-velocity model behind the 1–10 cm/yr band the readout calls typical: C. DeMets, R. G. Gordon & D. F. Argus, "Geologically current plate motions." Geophysical Journal International 181(1), 1–80, 2010.
The India–Eurasia collision that insight 1 and practice question 1 both use: P. Molnar & P. Tapponnier, "Cenozoic Tectonics of Asia: Effects of a Continental Collision." Science 189(4201), 419–426, 1975.

By the 42Math team · Updated 2026-05-21

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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Example problems

Atlantic-style spreading - 3000 km in 100 Myr → 3 cm/yr, printed alongside 30 mm/yr, and 1500 km more over the next 50 Myr
Pacific-style spreading - 6000 km in 120 Myr → 5 cm/yr, five times the slow case and near the top of the 1-10 cm/yr band the readout calls typical
Slow continental drift - 500 km in 50 Myr → 1 cm/yr, and even that covers 1000 km if you run it forward 100 Myr