Coriolis Force Calculation Example

Example data table

This example uses a one kilogram object moving eastward at 100 m/s, with no vertical velocity, at 45° north latitude.

Formula used

• F_C is the Coriolis force in newtons.
• m is mass in kilograms.
• Ω is angular velocity in radians per second.
• v is velocity in meters per second.
• φ is latitude in degrees, converted to radians internally.
• The calculator resolves signed east, north, and up components before finding total magnitude.

How to use this calculator

1. Enter the moving object’s mass and choose its unit.
2. Enter horizontal speed and select a matching speed unit.
3. Enter vertical velocity. Use zero for level motion.
4. Enter latitude using positive north and negative south values.
5. Enter the travel bearing measured clockwise from true north.
6. Keep Earth’s default angular velocity or enter another rotating system.
7. Select Calculate force and read signed vector components above the form.
8. Use CSV for a tabular record or PDF for a printable summary.

Understanding Coriolis force

Why it appears

Coriolis force is an apparent force. It appears inside a rotating reference frame. Earth rotates beneath objects that move through the atmosphere, oceans, or laboratory systems. An observer fixed to Earth can see a path bend even when no sideways contact force exists. The bend does not come from a new physical interaction. It comes from describing motion on a rotating planet.

Local coordinate system

The calculator uses a local east, north, up coordinate system. East points toward increasing longitude. North points toward the geographic pole. Up points away from Earth’s center. Horizontal speed and bearing create eastward and northward velocity components. A vertical velocity can also be entered. The program then combines those components with the rotation vector.

Latitude changes the result

Latitude matters because Earth’s rotation vector has different local directions around the globe. At the equator, the vertical part of the rotation vector is zero. At the poles, it is entirely vertical. This changes the force components. For horizontal motion, the familiar horizontal effect grows with the sine of latitude. It is zero at the equator and largest near either pole.

Direction and signed components

Direction matters as much as latitude. A northbound object can receive an eastward or westward component, depending on the hemisphere and motion. An eastbound object can gain a northward or southward component. The calculator reports signed east, north, and up forces. Positive values point east, north, or upward. Negative values point west, south, or downward.

Mass and speed scaling

Speed has a direct effect. Doubling speed doubles the calculated force. Mass also has a direct effect. Doubling mass doubles force, while the resulting acceleration stays unchanged. This is useful when comparing a lightweight parcel with a large aircraft. Their apparent accelerations can match when their velocities and positions match, although their forces differ.

Using another rotating system

Earth’s angular velocity is set to a standard value by default. You can replace it for a rotating platform, a centrifuge, or another planet. Use radians per second. Keep all inputs physically consistent. The calculator converts selected mass and speed units to SI values before evaluating the vector expression.

Reading the output

Results include total force, horizontal force, force components, and acceleration components. The horizontal bearing of the force is also shown when it can be determined. A small result is normal for short, slow motions. The effect becomes important for long travel times, large distances, fast vehicles, winds, ocean currents, and ballistic trajectories.

A useful test case

Use a test first. Set mass to one kilogram, horizontal speed to one hundred metres per second, vertical velocity to zero, latitude to forty-five degrees, and bearing to ninety degrees. Compare component signs after reversing the bearing. This practice makes the coordinate convention easier to trust.

Limits of a first estimate

This tool does not replace a complete trajectory model. Real systems may involve gravity, drag, pressure gradients, thrust, friction, curvature, and changing latitude. Still, the computed value gives a clear first estimate. It also helps check signs, units, and expected direction before building a more detailed model.

FAQs