The Coriolis effect is not a force in the usual sense. It is the apparent sideways acceleration that a freely moving object seems to acquire when its motion is described from a frame of reference that is itself rotating — in the everyday case, the surface of the Earth. Nothing pushes the object. The ground beneath it turns, and from the ground's point of view the object curves.
Arb Digital publishes free physics calculators that state their assumptions and refuse to overstate their results. This page computes the standard horizontal Coriolis relation for a mass moving over the Earth's surface, and it is equally concerned with telling you where the effect is genuinely large — weather systems, ocean currents, long-range ballistics — and where the popular story about it is simply wrong.
What This Coriolis Effect Calculator Does
You enter a latitude, a horizontal speed, a mass and a travel distance. The tool returns the Coriolis force on the mass, the Coriolis parameter for that latitude, the resulting acceleration, the lateral deflection accumulated over the distance travelled, and the inertial period — the time a freely moving parcel would take to complete one circle under Coriolis alone.
The Earth's rotation rate is an editable input rather than a buried constant, so the arithmetic is visible and the same page can be pointed at another rotating body. The default is the sidereal value, one rotation relative to the fixed stars rather than relative to the Sun.
Note what the mass does and does not change. It scales the force, because force is mass times acceleration, but the acceleration and the deflection are independent of it. A cannon shell and a rifle bullet fired at the same speed over the same distance drift sideways by the same amount, which is one of the more counter-intuitive things about the effect and follows directly from the algebra below.
How to Use It
- Enter latitude with its sign. Positive north, negative south. The sine of the latitude carries the hemisphere, and getting it wrong reverses the direction of the deflection.
- Use the horizontal component of the speed. The relation modelled here is for horizontal motion over the surface. Vertical motion couples to the horizontal component of the rotation vector, which is a separate term this page does not compute.
- Set the travel distance to the path length, not the straight-line displacement. The deflection accumulates over the time in flight, and the time comes from the distance divided by the speed.
- Read the deflection alongside the acceleration. The acceleration can look tiny and the deflection still be significant if the flight is long, because the deflection grows with the square of time.
- Compare a case against the equator preset. Watching the whole effect go to zero at zero latitude is the fastest way to internalise why this is a latitude-dependent phenomenon rather than a global constant.
The Formula: How the Coriolis Effect Is Calculated
Write the Earth's angular rotation rate as Ω and the latitude as φ. The Coriolis parameter, the quantity meteorologists actually use, is
f = 2Ω sinφ
and it has units of inverse seconds. For an object moving horizontally at speed v, the horizontal Coriolis acceleration is a = f v and the force on a mass m is F = m f v = 2mΩv sinφ. The deflection accumulated over a flight time t, treating the acceleration as roughly constant and perpendicular to the motion, is y ≈ ½ f v t², and substituting t = R/v for a range R gives y ≈ f R² / (2v) — note that a faster projectile drifts less over the same range, because it spends less time in flight.
Work the defaults. At 45° north, sinφ = 0.7071, so f = 2 × 7.2921 × 10⁻⁵ × 0.7071 = 1.0313 × 10⁻⁴ s⁻¹. At a speed of 800 m/s the acceleration is 1.0313 × 10⁻⁴ × 800 = 0.0825 m/s², and on a 10 kg mass the force is 0.825 N. Over 1,000 m the flight lasts 1.25 s, so the deflection is ½ × 0.0825 × 1.25² = 0.064 m, about six and a half centimetres. That is real for a target shooter and irrelevant for almost anything else at that range.
The inertial period is 2π/f, which at 45° works out at about 16.9 hours. This is the period of an inertial circle in the ocean, and the closely related concept of the Foucault pendulum's precession period comes from the same sinφ dependence. The treatment of the effect as a fictitious force arising in a rotating frame is set out on the Georgia State University HyperPhysics page on centrifugal and Coriolis forces.
Why the Effect Depends on Latitude
The sinφ factor is the heart of it, and it is worth seeing why it is there rather than accepting it.
The Earth rotates about an axis through the poles. At the North Pole, the ground under your feet is turning about a vertical line: the local horizontal plane spins like a turntable, and any object moving across it curves. At the equator the rotation axis lies in the local horizontal plane, so the ground does not spin about the vertical at all — the local horizontal plane tips rather than turns — and the horizontal Coriolis effect vanishes entirely. In between, only the component of the rotation vector along the local vertical matters, and that component is Ω sinφ.
The consequences are visible in the atmosphere. Tropical cyclones do not form within roughly five degrees of the equator, because there is too little Coriolis parameter for a low-pressure area to organise into a rotating system. Away from that band, air moving toward low pressure is deflected until it circles rather than converging directly, which is why weather systems rotate anticlockwise in the northern hemisphere and clockwise in the southern one. The same balance, between the pressure gradient and the Coriolis term, is what makes the geostrophic wind blow along the isobars rather than across them, and it is described in NOAA's JetStream online school for weather.
The Bathtub Myth, Stated Plainly
The Coriolis effect does not determine which way water rotates as it drains from a sink, a bath or a toilet. This is the most widely repeated piece of misinformation in popular physics, and the calculator above is the fastest way to see why.
Set the latitude to 45°, the speed to 0.1 m/s, the mass to 1 kg and the distance to 0.3 m — a plausible drain. The Coriolis acceleration comes out around 10⁻⁵ m/s², roughly a millionth of gravity, acting for about three seconds. The resulting deflection is a small fraction of a millimetre. Meanwhile the water carries residual circulation from how the basin was filled, from the shape of the outlet, from the last time anything touched it, and from the asymmetry of the vessel itself. Every one of those is orders of magnitude larger.
The effect can be demonstrated in a domestic basin, but only under laboratory discipline: a symmetrical circular tank, filled with great care, then left covered and undisturbed for many hours so that residual motion decays away, and drained slowly. Experiments of that kind have been done in both hemispheres and the sense of rotation does follow the hemisphere. What that shows is that the effect is real and correctly signed, not that it governs an ordinary sink. A bath that has just had someone in it retains circulation many thousands of times stronger than the Coriolis term.
The related claim that water spins opposite ways on either side of a line painted on the ground at the equator, demonstrated to tourists for a small fee, is a conjuring trick. The operator pours the water with a swirl, and the direction is set by the pouring.
Where the Effect Genuinely Matters
Long-range gunnery corrects for it. A naval shell in flight for a minute or more accumulates a deflection of tens of metres, which is the difference between a hit and a miss, and firing solutions have included a Coriolis term for over a century. Long-range rifle shooting at a thousand yards sees a drift of a few centimetres, small but not negligible against a target of that size.
Atmospheric and oceanic circulation is dominated by it at large scale. The trade winds, the westerlies, the gyres of the major ocean basins and the Ekman spiral in the surface layer are all Coriolis phenomena. Ballistic missiles and orbital launches account for it as a matter of course. Foucault's pendulum makes it directly visible: the plane of swing precesses at a rate proportional to sinφ, taking about 32 hours at 45° latitude and exactly one sidereal day at the pole.
The common thread is scale. The effect is weak per unit time but it acts continuously, so it dominates whenever the motion lasts long enough or covers enough ground. That is why it rules the atmosphere and ignores your plumbing.
Where This Sits Among the Other Motion Tools
This page handles one apparent force in a rotating frame. For circular motion in an inertial frame use the centripetal force calculator, and for the rotational quantities themselves the angular velocity calculator and the angular acceleration calculator. General force and acceleration arithmetic sits in the force calculator, the net force calculator and the acceleration calculator. Flight times come from the speed distance time calculator, and the pendulum whose precession makes this effect visible is handled by the simple pendulum calculator.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Applying it to bathtubs and toilets — the Coriolis acceleration at domestic scale is around a millionth of gravity and is swamped by residual circulation, basin shape and outlet geometry by many orders of magnitude.
- Forgetting the sign of the latitude — the deflection is to the right of the motion in the northern hemisphere and to the left in the southern one, and a missing minus sign reverses the answer.
- Expecting a heavier object to drift more — the force scales with mass but the acceleration does not, so two projectiles at the same speed over the same range deflect identically.
- Assuming a faster projectile drifts further — over a fixed range it drifts less, because the deflection depends on the square of the flight time and speed shortens the flight.
- Using a solar day for the rotation rate — the Earth turns once per sidereal day of 23 hours 56 minutes, and using 24 hours introduces a small but pointless error.
Related Free Tools From Arb Digital
Work rotating-frame problems alongside the centripetal force calculator, the angular velocity calculator and the angular acceleration calculator. Handle straightforward dynamics with the force calculator, the net force calculator and the acceleration calculator. Get flight times from the speed distance time calculator and periods from the simple pendulum calculator. Every free tool Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
For horizontal motion over the Earth's surface the force is two times the mass, times the rotation rate, times the speed, times the sine of the latitude. The rotation-rate and latitude part is grouped as the Coriolis parameter f = 2 x omega x sine of latitude, and the acceleration is simply f times the speed.
No. At domestic scale the Coriolis acceleration is around a millionth of gravity, and the deflection over a few seconds of draining is a fraction of a millimetre. Residual circulation from filling the basin, the shape of the vessel and the geometry of the outlet are all thousands of times stronger and decide the direction entirely.
Because only the component of the Earth's rotation vector along the local vertical produces a horizontal deflection, and that component is the rotation rate times the sine of the latitude. At the equator the rotation axis lies in the local horizontal plane, the sine is zero, and the horizontal Coriolis term disappears.
No. Mass scales the force but cancels out of the acceleration, so two objects moving at the same speed over the same distance at the same latitude drift sideways by exactly the same amount regardless of how heavy they are.
To the right of the direction of motion in the northern hemisphere and to the left in the southern hemisphere. That is why low-pressure systems circulate anticlockwise north of the equator and clockwise south of it, and it is carried in the calculation by the sign of the latitude.
Two pi divided by the Coriolis parameter, which is the time a freely moving parcel would take to complete one circle under the Coriolis term alone. It is about 16.9 hours at 45 degrees latitude and shortens toward 12 hours at the poles, and it sets the timescale of inertial oscillations in the ocean.
Yes, at long range. A rifle shot at a thousand yards drifts a few centimetres, and a naval shell in flight for a minute or more drifts tens of metres. Firing solutions have included the correction for well over a century, though it is negligible at ordinary ranges.
This tool is provided for educational use only. It computes the standard horizontal Coriolis relation for a mass moving over a rotating sphere and ignores drag, wind, the vertical Coriolis term, the curvature of the path and every other force acting on a real object. It is not a ballistic solution, a navigation aid or a weather product, and it must not be used for any operational purpose.
