By Zencalcy Editorial TeamLast reviewed About us
When two velocities act on the same object, they add as vectors. The size of the resultant depends on the angle between them: parallel velocities add directly, opposite ones subtract, and perpendicular ones combine through Pythagoras.
Add two velocities into one resultant vector.
R = √(v₁² + v₂² + 2v₁v₂cos θ) φ = atan2(v₂ sin θ, v₁ + v₂ cos θ)
The direction φ is measured from the first velocity. The formula is the law of cosines applied to velocity vectors.
| Symbol | Meaning |
|---|---|
| v₁, v₂ | The two velocities, in metres per second. |
| θ | Angle between the velocity vectors. |
| R | Resultant velocity, in metres per second. |
| φ | Direction of the resultant relative to v₁. |
Perpendicular vectors give √(9 + 16) = 5 m/s at atan(4/3) = 53.13° from the first velocity.
Continue with the Rolling Resistance Calculator, Sled Ride Calculator, or the SUVAT Calculator — or browse more kinematics tools and all physics calculators.
At 180° the cosine is −1 and the resultant is the difference of the speeds, pointing along the larger one.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026