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y-Component from Magnitude and Angle

vy=∣v⃗∣sin⁡θv_y = |\vec{v}| \sin\theta
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Worked example: Magnitude 20 at 30° → v_y = 10. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

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Direction Angle of a 2D VectorAngle Between Two 2D Vectors (Components)Dot Product of Two 2D Vectors (Components)Dot Product of Two 3D Vectors (Components)
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See also

Direction Angle of a 2D Vector: Both use vector y component and angle from +x axis.x-Component from Magnitude and Angle: Both use vector magnitude and angle from +x axis.Magnitude of a 2D Vector: Both use vector y component and vector magnitude.Magnitude of a 3D Vector: Both use vector y component and vector magnitude.Angle Between Two 2D Vectors (Components): Both use vector y component.Cross Product z-Component of Two 2D Vectors: Both use vector y component.
8 more relatedDot Product of Two 2D Vectors (Components): Both use vector y component.Dot Product of Two 3D Vectors (Components): Both use vector y component.Cross Product Magnitude: Both use vector magnitude.Dot Product from Magnitudes and Included Angle: Both use vector magnitude.Magnitude of a Scaled Vector: Both use vector magnitude.Resultant of Two Vectors at an Angle: Both use vector magnitude.Scalar Projection of One Vector onto Another: Both use vector magnitude.Unit Vector Component (Normalization): Both use vector magnitude.
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y-Component from Magnitude and Angle explained

θvy|v|

The vertical partner of the x-component: |v| sin θ is how much of the arrow points up. A projectile launched at 40 m/s and 30° leaves the muzzle with 40 × sin 30° = 20 m/s of upward speed, and that number alone, not the 40, decides how high and how long it flies. Together the pair (|v| cos θ, |v| sin θ) is the machinery that lets you replace one awkward diagonal with two independent one-dimensional problems, which is the reason vectors earn their place in physics at all.

Solving for the angle uses arcsin, whose principal branch runs only from −90° to 90°. A vector at 150° has the same y-component as one at 30°, so formula.expert returns the first-quadrant answer; if you know the vector leans left, its true direction is 180° minus what you get. When the whole vector is horizontal, sin θ = 0 and no y-component can tell you how long it is.

y-Component from Magnitude and Angle formula

vy=∣v⃗∣sin⁡θv_y = |\vec{v}| \sin\theta
Where
  • vyv_y= y-component
  • ∣v⃗∣|\vec{v}|= Vector magnitude
  • θ\theta= Angle from +x axis (°)
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Vector operations

12 formulasMagnitude, direction, components and unit vectors, plus the dot and cross products and the projections and angles they give you.

Revised 31 October 2026
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formula.expert. (2026, October 31). y-Component from Magnitude and Angle Formula & Calculator. https://formula.expert/solvers/vector-y-component

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