Coriolis Effect Calculator

Calculation mode: The physics setup used by the calculator. Earth mode uses latitude, while general mode uses the angle between motion and the rotation axis.

Coriolis effect: An apparent sideways deflection seen when motion is described in a rotating frame rather than a non-rotating one.[1]

Coriolis acceleration magnitude: The size of the sideways acceleration caused by motion in the rotating frame. It is always shown as a nonnegative magnitude here.

Coriolis force magnitude: The apparent force found from mass times Coriolis acceleration. Mass changes force, but not the acceleration itself.[1][3]

Estimated sideways deflection: The approximate sideways distance after the chosen travel time, using a constant-acceleration estimate.

Deflection direction: A plain-language note about which way the path bends. In Earth mode, this depends on hemisphere and heading; in a general rotating system, the deflection is perpendicular to the motion and rotation-axis geometry.

Coriolis parameter: In Earth mode, this is f, a signed value based on latitude. It is 0 at the equator and changes sign between hemispheres.

Angular speed (rad/s): How fast the body or frame rotates. Earth mode uses Earth's mean angular speed by default.[3]

Mistake: Entering a Latitude (deg) outside -90 to 90.
Fix: Keep Latitude (deg) between -90 and 90. Use positive values for north and negative values for south.

Mistake: Typing a negative value for Speed relative to rotating surface (m/s) or Travel time (s) .
Fix: Enter 0 or more for both fields. Direction should be described with Motion heading , not by making speed negative.

Mistake: Filling in Mass (kg, optional for force) with 0 or a negative number and expecting a valid Coriolis force magnitude .
Fix: Leave Mass (kg, optional for force) blank if you do not need force, or enter a value greater than 0.

Mistake: Using Latitude (deg) to control the result in General rotating system mode.
Fix: In that mode, the important advanced input is Angle between motion and rotation axis (deg) . Hidden Earth-only inputs should not be used.

Mistake: Entering an Angle between motion and rotation axis (deg) outside 0 to 180.
Fix: Keep that angle from 0 to 180. A value of 90 deg gives the largest Coriolis acceleration magnitude , while 0 deg or 180 deg gives 0.

Mistake: Reading Estimated sideways deflection as an exact path prediction.
Fix: Treat Estimated sideways deflection as a simple constant-acceleration estimate over the chosen Travel time (s) , not a full trajectory simulation.

• This calculator reports magnitudes for Coriolis acceleration magnitude, Coriolis force magnitude, and Estimated sideways deflection, so those outputs do not carry a plus or minus sign.
• Estimated sideways deflection uses a simple constant-acceleration model, so it does not track a changing path, changing heading, drag, lift, or other forces.
• In Earth surface mode, the formula is the common surface-level simplification based on Latitude (deg). It is most useful for educational estimates, not full geophysical modeling.
• The Deflection direction note in Earth mode is simplified. For northward or southward motion, the full 3D Coriolis direction depends on the full velocity vector, so the note is intentionally less specific.
• If Mass (kg, optional for force) is blank, Coriolis force magnitude is shown as N/A because force cannot be computed without mass.
• If Angular speed (rad/s) is 0, all Coriolis-based results become 0 except force still remains N/A when mass is blank.
• Inputs must stay in physical bounds: Latitude (deg) from -90 to 90, Angle between motion and rotation axis (deg) from 0 to 180, and nonnegative speed and travel time.

Core idea

The Coriolis effect is treated here as an apparent deflection seen in a rotating coordinate system.[1] The calculator separates three different things: acceleration, force, and estimated sideways distance.

Formulas used

a = 2 * ω (angular speed in rad/s) * v (speed in m/s) * |sin(φ)|

Use this Earth-surface form when motion is along the rotating surface and φ is Latitude (deg).

a = 2 * ω (angular speed in rad/s) * v (speed in m/s) * |sin(θ)|

Use this general rotating-system form when θ is the Angle between motion and rotation axis (deg). This comes from the magnitude of the Coriolis term and is largest when motion is perpendicular to the rotation axis.[3]

F = m (mass in kg) * a

Coriolis force magnitude is shown only when mass is provided.

d = 0.5 * a * t^2

This gives Estimated sideways deflection for constant Coriolis acceleration over Travel time (s).

f = 2 * ω (angular speed in rad/s) * sin(φ)

In Earth mode, this is the Coriolis parameter. It keeps its sign, so it is positive in the Northern Hemisphere and negative in the Southern Hemisphere.

Worked mini-example

Suppose you use Earth mode with speed 250 m/s, latitude 45 deg, mass 1000 kg, travel time 3600 s, and Earth's default angular speed 7.2921159 x 10^-5 rad/s.[3]

a = 2 * 7.2921159 x 10^-5 * 250 * |sin(45 deg)| = 0.02578 m/s^2

F = 1000 * 0.02578 = 25.78 N

d = 0.5 * 0.02578 * 3600^2 = 167067.64 m

f = 2 * 7.2921159 x 10^-5 * sin(45 deg) = 1.031 x 10^-4 1/s

This means the sideways acceleration is small, but over a long time the simple deflection estimate can become very large.

Direction logic

In Earth mode, the direction note is written in plain language to help beginners. A common rule is that motion appears deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.[1] For eastward or westward travel, the calculator gives a clearer horizontal note; for northward or southward travel, it gives a simplified note instead of pretending to show the full 3D vector.

Assumptions used in the math

The formulas assume constant speed, constant latitude or constant axis angle, and constant angular speed during the chosen time interval. They also treat the sideways distance with a basic constant-acceleration estimate rather than a full trajectory integration, so real paths can differ when other forces or changing geometry matter.