Coriolis Effect Calculator finds the Coriolis force and acceleration from mass, speed and latitude, with bullet drift in MOA and mils, the Coriolis parameter and the Eötvös effect.
Latitude sets the strength: zero on the equator, greatest at the poles.
Rotation, Distance, Units
The rotation rate is set to Earth. Change it for another planet or a turntable.
Step-by-Step Calculation
- Mass in kilograms: m = 50,000 kg
- Velocity in meters per second: v = 500 km/h = 138.889 m/s
- Latitude: φ = 51.5° N, so sin φ = 0.782608
- Rotation rate: ω = 7.292115 × 10⁻⁵ rad/s
- F = 2 × m × v × ω × sin φ = 2 × 50,000 × 138.889 × 7.292115 × 10⁻⁵ × 0.782608 = 792.6 N
Effect at Other Latitudes
| Latitude | Force (N) | Share of max |
|---|---|---|
| 0° | 0 | 0% |
| 15° | 262.1 | 25.88% |
| 30° | 506.4 | 50% |
| 45° | 716.2 | 70.71% |
| 51.5° | 792.6 | 78.26% |
| 60° | 877.1 | 86.6% |
| 75° | 978.3 | 96.59% |
| 90° | 1,013 | 100% |
Drift at Other Distances
| Distance | Drift (m) | Time |
|---|---|---|
| 5 km | 10.27 | 36 s |
| 10 km | 41.09 | 72 s |
| 20 km | 164.4 | 2.4 min |
| 50 km | 1,027 | 6 min |
| 100 km | 4,109 | 12 min |
Deflection Diagram
The moving object curves to the right of its intended path in the Northern Hemisphere. The curve is exaggerated to be visible.
Coriolis Effect Calculator for Force and Drift
The Coriolis Effect Calculator finds the sideways force on anything that moves over a rotating surface. Its default is an aircraft of 50,000 kg flying at 500 km/h over London, at latitude 51.5° N. The result is 792.6 N pushing to the right of travel.
The Calculate list has six choices. Coriolis Force is the main one, and Bullet or Projectile Drift turns the same physics into a hold for a long shot. The other four work backward to the mass, the velocity, the rotation rate or the latitude that would produce a given force.
Four cards sit under the main answer of the Coriolis Effect Calculator. They give the Coriolis acceleration and its direction, the sideways drift over a distance you choose, the Coriolis parameter with a Rossby number, and the vertical part of the effect on an object heading east or west.
How to Calculate the Coriolis Effect
The Coriolis force depends on four things. They are the mass of the object, its speed over the ground, the rotation rate of the planet and the sine of the latitude. The mathematical formula for the Coriolis force in the horizontal plane is below.
$$F = 2 m v \omega \sin \varphi$$
Here m is in kilograms, v is in meters per second, ω is in radians per second and φ is the latitude. Dividing by the mass leaves the Coriolis acceleration, which is the same for a feather and an airliner moving at the same speed.
$$a = 2 v \omega \sin \varphi$$
For the default, 500 km/h is 138.889 m/s and the sine of 51.5° is 0.7826. The force is 2 × 50,000 × 138.889 × 7.292115 × 10⁻⁵ × 0.7826, which is 792.6 N. The acceleration is 0.01585 m/s², only 0.1616% of gravity.
The Coriolis Effect Calculator presets the rotation rate to Earth at 7.292115 × 10⁻⁵ rad/s, the mean angular velocity listed by the International Earth Rotation Service. That is one turn per sidereal day of 86,164 s. Using a 24 hour day instead gives 7.272 × 10⁻⁵ and an answer about 0.3% too low.
Where the Coriolis Effect Is Strongest
The Coriolis effect is at its maximum at the North and South Poles, where the sine of the latitude is 1. It is weakest near the equator and exactly zero on it, where the sine is 0. Halfway up, at 30°, it is already half of the polar value.
| Latitude | Share of polar maximum | Coriolis parameter f | Force on the default aircraft |
|---|---|---|---|
| 0° (equator) | 0% | 0 | 0 N |
| 15° | 25.88% | 3.775 × 10⁻⁵ s⁻¹ | 262.1 N |
| 30° | 50% | 7.292 × 10⁻⁵ s⁻¹ | 506.4 N |
| 45° | 70.71% | 1.031 × 10⁻⁴ s⁻¹ | 716.2 N |
| 60° | 86.6% | 1.263 × 10⁻⁴ s⁻¹ | 877.1 N |
| 75° | 96.59% | 1.409 × 10⁻⁴ s⁻¹ | 978.3 N |
| 90° (pole) | 100% | 1.458 × 10⁻⁴ s⁻¹ | 1,013 N |
The reason there is no Coriolis effect on the equator is geometry. The sideways force comes from the part of Earth’s spin that turns the ground under you, like a turntable. At a pole the ground turns once a day about the vertical. On the equator the ground only tips over and does not turn at all.
That is also why hurricanes need some distance from the equator to start spinning. NOAA’s hurricane research division puts the minimum at about 300 miles. At that distance the latitude is 4.3° and the Coriolis effect is only 7.6% of its polar strength.
Coriolis Parameter Formula
Meteorologists and oceanographers fold the rotation rate and latitude into one number, the Coriolis parameter or Coriolis frequency. The formula for calculating the Coriolis parameter is twice the rotation rate times the sine of the latitude.
$$f = 2 \omega \sin \varphi$$
The third card of the Coriolis Effect Calculator reports it. At 51.5° N it is 0.0001141 s⁻¹, which is 78.26% of the polar maximum. By convention f is positive in the Northern Hemisphere and negative in the Southern, so choosing °S flips its sign.
Two more results come from f. The inertial period is 2π ÷ f, the time a freely drifting parcel of water or air takes to complete one loop. It is 15.29 hours at 51.5°, 11.97 hours at a pole and 23.93 hours at 30°.
The inertial circle radius is the speed divided by f. For the default aircraft it is 1,217 km. An object left to coast at that speed would curl around a circle of that size, with the Coriolis force acting as the centripetal force. The Circular Motion Calculator links the radius, speed and period of such a loop.
Which Direction Is the Coriolis Effect
The deflection is to the right of travel in the Northern Hemisphere and to the left in the Southern Hemisphere. It does not matter whether the object heads north, south, east or west. The first card states the side, and the Deflection Diagram draws the curved path.
This rule for winds is often called Ferrel’s law, and it is the nearest thing to a “Coriolis law”. Whether the Coriolis force looks clockwise or anticlockwise depends on what you watch. A single moving object in the north curves clockwise, because it keeps turning right.
A storm does the opposite. Air rushing inward toward low pressure is turned right on every side, and that sets the whole system spinning. Hurricanes rotate counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere, as NOAA and National Geographic both describe.
At What Distance the Coriolis Effect Matters
The force is always small, so distance and time decide whether it shows. Sideways drift grows with the square of the distance at a fixed speed. Open Rotation, Distance, Units and set Travel Distance to see it.
$$d = \frac{\omega \sin \varphi \times D^2}{v}$$
The default aircraft drifts 41.09 m over 10 km, which takes 72 s. Over 1 km the drift is only 0.4109 m, a hundred times less for a tenth of the distance. The Drift at Other Distances table in the Coriolis Effect Calculator lists five distances around your own.
The Rossby number on the third card is the standard test of whether the effect matters. It is the speed divided by the Coriolis parameter times the distance. A value far above 1 means the Coriolis effect is minor, and a value near or below 1 means it controls the motion.
$$Ro = \frac{v}{f d}$$
The default aircraft has a Rossby number of 121.7 over 10 km, so the drift is a small correction. Over 1,000 km it falls to 1.217. A storm with 10 m/s winds across 500 km at 20° latitude comes to 0.4, which is why weather systems rotate. A rifle shot of 1,000 yards sits near 5,800.
A sink is at the far end of the scale. Water moving at 0.1 m/s across a 0.3 m basin at 45° latitude has a Rossby number above 3,000 and drifts 0.046 mm. That is why the Coriolis effect does not affect toilets or sinks. The Library of Congress gives the same answer, and says the drain shape and the way the water entered decide the swirl.
The drift formula assumes the drift stays small next to the distance. It is sound for bullets, shells, short aircraft legs and lab turntables. Once the drift passes 10% of the distance, the drift card turns amber and the note reads Drift Estimate Past Its Range. For the default aircraft that happens beyond about 243 km, where the path is a curve and the straight-line estimate overstates the drift.
Coriolis Effect on a Bullet
To calculate the Coriolis effect on a bullet, set Calculate to Bullet or Projectile Drift. Enter the range, the time of flight, the latitude and the direction of fire. The Coriolis effect sniper equation for sideways drift needs only three of them.
$$d = \omega X t \sin \varphi$$
Here X is the range in meters and t is the time of flight in seconds. A 1,000 yard shot with a 1.5 s flight at 51.5° N drifts 7.828 cm to the right, which is 3.082 inches. The second card turns that into a windage hold of 0.2943 MOA, or 0.0856 mil, to the left of the target.
The hold in MOA has a shortcut. It is about 0.25 times the time of flight times the sine of the latitude, and the range drops out. Convert between MOA, mils and inches at any range with the MOA Calculator.
So the Coriolis effect does affect snipers, but only at long range. The table uses a 45° latitude and an average bullet speed of 2,000 ft/s. If you know the speed and not the flight time, switch the time box to Average Speed and the range is divided by the speed for you.
| Range | Time of flight | Sideways drift | Windage hold |
|---|---|---|---|
| 300 yd | 0.45 s | 0.25 in (0.64 cm) | 0.08 MOA |
| 500 yd | 0.75 s | 0.70 in (1.77 cm) | 0.13 MOA |
| 1,000 yd | 1.5 s | 2.78 in (7.07 cm) | 0.27 MOA |
| 1,500 yd | 2.25 s | 6.26 in (15.91 cm) | 0.40 MOA |
| 2,000 yd | 3.0 s | 11.14 in (28.29 cm) | 0.53 MOA |
Under 500 yards the drift is less than an inch and is lost in wind and group size. Past 1,000 yards it is several inches and worth dialing. Real bullets slow down, so their flight times at long range are longer than this constant-speed table. The Ballistic Coefficient Calculator helps with downrange speed.
The sideways drift is the same whichever way the shot is fired. Only the vertical shift changes with direction, which the Coriolis Effect Calculator shows in the Shift by Direction of Fire table for all eight compass points.
Eötvös Effect on Bullets and Aircraft
Earth’s spin also has a vertical effect, named after the Hungarian physicist Loránd Eötvös. An object moving east is moving with the planet’s rotation, so it is thrown outward slightly more and feels lighter. Moving west it feels heavier.
$$h = \omega X t \cos \varphi \sin A$$
Here A is the direction of fire measured clockwise from north. The Eötvös effect on bullets is largest on the equator and for shots due east or west. The default shot, fired east at 51.5° N, lands 6.226 cm high. The fourth card gives the elevation hold as 0.2341 MOA low.
For the default aircraft, the fourth card leads with the vertical Coriolis part, 630.5 N of lift when heading east. That is the part that flips sign with direction. The full Eötvös formula used in gravity surveys adds a second term, the speed squared divided by Earth’s radius, which lightens the load in every direction.
$$a = 2 \omega v \cos \varphi \sin A + \frac{v^2}{R}$$
At 500 km/h the second term is 0.003 m/s², or about 151 N for this aircraft. The two rows on the card give the totals, 781.9 N lighter heading east and 479.1 N heavier heading west. They use Earth’s mean radius of 6,371 km, so they appear only while the rotation rate is left at Earth’s value.
Solving for Mass, Speed, Spin or Latitude
The four reverse choices rearrange the force formula. Each starts from a force, 1,000 N by default, with the other default entries left as they are. They suit physics problems that give the force and ask for one of the inputs.
| Calculate | Formula | Default result |
|---|---|---|
| Mass | m = F ÷ (2 v ω sin φ) | 63,082 kg |
| Velocity | v = F ÷ (2 m ω sin φ) | 175.2 m/s (630.8 km/h) |
| Angular Velocity | ω = F ÷ (2 m v sin φ) | 9.2 × 10⁻⁵ rad/s, one turn every 18.97 h |
| Latitude | φ = asin(F ÷ (2 m v ω)) | 80.88° north or south |
The latitude choice has a limit. The largest force the default aircraft can feel, at a pole, is 1,013 N. Ask for more than that and the Coriolis Effect Calculator reports that no latitude gives it.
The rotation rate is editable, so the Coriolis Effect Calculator also handles another planet or a lab turntable. It accepts rad/s, RPM and degrees per hour. The Angular Velocity Calculator converts a rotation period into any of those. On a turntable, use 90° as the latitude so the sine is 1.
Cause, Name and Real-Life Examples
The main cause of the Coriolis effect is that Earth rotates while things move across it. The ground at the equator travels east at about 1,674 km/h, and the ground near a pole barely moves. An object keeps the eastward speed it started with, so it drifts off line as the ground beneath changes speed.
How do you explain the Coriolis effect in a simple way?
Picture two children on a spinning merry-go-round. One rolls a ball straight toward the other. While the ball rolls, the second child is carried sideways, so the ball misses. To the children it looks as if the ball curved. To someone standing on the ground, the ball went straight and the children moved.
Is the Coriolis effect an illusion?
It is an apparent force and not a push from any object. Physics calls it an inertial force, a fictitious force or a pseudo force, and those are its other names. The deflection is still real for anyone measuring from the rotating Earth, so it must be included in the sums. The Centrifugal Force Calculator covers the other inertial force of a spinning frame.
Why is it called Coriolis, and who discovered it?
It is named after the French engineer Gaspard-Gustave de Coriolis, born in Paris in 1792. Britannica dates his description of the force to an 1835 paper on the equations of relative motion of systems of bodies. He also gave work and kinetic energy their modern meanings.
What is a real-life example of the Coriolis effect?
Weather gives the clearest examples. Hurricanes and cyclones spin because of it. The trade winds blow from the northeast instead of straight toward the equator. Ocean currents form large loops, long-range artillery and sniper shots need a correction, and Jupiter’s fast spin stretches its winds into east-west bands.
Does the Coriolis effect cause wind or affect airplanes?
It does not cause wind. Differences in air pressure do that. The Coriolis effect turns the wind once it is moving, which shapes the prevailing wind belts. For airplanes the direct force is tiny, 0.16% of gravity in the default example. Pilots feel it mostly through those winds on long routes.
What would happen if there were no Coriolis effect?
Air would flow straight from high pressure to low pressure, and each low would fill in a short time. There would be no spinning hurricanes, no trade winds or westerlies as we know them, and no large ocean gyres. A planet that did not rotate would have exactly this, since the rotation rate in the formula would be zero.
Is Coriolis force in JEE?
The Coriolis force is not named in the JEE physics syllabus. The mechanics units list frames of reference, Newton’s laws, uniform circular motion and centripetal force. Rotating frames with a Coriolis term belong to first-year university mechanics, where this calculator matches the standard formula.
The Coriolis force is one of several effects that appear only in a spinning frame. More tools for spinning systems, from angular speed to circular paths, are grouped on the Rotational Motion Calculators hub.