Horizontal Coriolis Force, Acceleration and Signed Latitude

Formula and method

At signed latitude 90°, a 1 kg object moving at 3.6 km/h (1 m/s) with the nominal Earth rotation reference gives F=0.000145842302934128 N and a=0.000145842302934128 m/s².

F = 2mΩv sin φ; a = F/m.

Worked example

Enter these known values and leave the other values blank.

Assumptions and limitations

• This is a signed horizontal scalar model, not the full three-dimensional −2m Ω×v vector. For positive Ω and v, the sign follows signed latitude. A force magnitude is the absolute value. Horizontal Coriolis acceleration is zero at the equator; this does not eliminate every possible vertical component of the full vector.
• Use latitude from −90° to +90°, signed velocity/rotation consistently, and positive object mass. The latitude inverse uses the principal asin branch in that latitude interval. An impossible sine ratio is rejected rather than returning a complex value.
• The initial Earth angular rate is the IERS conventional nominal 7.2921151467064 × 10⁻⁵ rad/s, an epoch-1820 reference convention. It is editable for another rotating frame and is not a live measured Earth-orientation value. RPM uses exactly 2π radians per revolution, and Hz means complete revolutions per second here.
• Changing the hemisphere selector changes only the contextual direction note; it does not change signed latitude or numerical outputs. Choose the note context to match latitude. Its right/left statement assumes Earth’s normal positive rotation and non-equatorial horizontal motion.
• Zero rotation, velocity or signed latitude gives zero horizontal scalar and acceleration when the other required quantities are known. Two zero force/acceleration values do not identify mass; zero products can leave other inverses nonunique. Clear an unknown before solving; acceleration follows the captured force/mass relation and requires known positive mass.
• This algebraic relationship does not integrate a trajectory or predict a landing point; geometry, Earth orientation and other forces require a more complete dynamical model.

Common questions

References

• NASA GMAO: Coriolis parameter in the horizontal equations
• IERS: Earth rotation constants and reference convention
• NIST Handbook 44: exact unit definitions
• Calculation definition and unit reference

Use positive mass for a material object, enforce the signed scalar sine bound and reject a nonzero Coriolis scalar paired with a zero rotation, velocity, latitude or acceleration. Zero rotation, velocity, latitude, force and acceleration remain valid where physically consistent. Correct the captured reversed angular-unit selector: RPM and Hz convert to radians per second by 2π radians per revolution, rather than swapping the conversion factors. Skip five nonunique or singular inverse branches in the signed scalar model, including zero-force inverses that cannot identify a positive mass. The latitude inverse uses the principal sine branch only when its ratio is real. Other independently determinate captured equations remain available. Use the IERS conventional nominal angular velocity 7.2921151467064 × 10⁻⁵ rad/s as the editable initial Earth reference, replacing 7.27 × 10⁻⁵. This is the epoch-1820 reference convention, not a current measured rotation rate. Bookify uses the exact relationship one revolution = 2π radians instead of the captured rounded angular-speed factor. Feet per second squared use exactly 0.3048 meters per second squared, replacing a rounded reciprocal factor.

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