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x-Component from Magnitude and Angle

vx=∣v⃗∣cos⁡θv_x = |\vec{v}| \cos\theta
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Worked example: Magnitude 10 at 60° → v_x = 5. Press Try an example to run it live, then adjust anything.

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Where x-Component from Magnitude and Angle fits

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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 x component and angle from +x axis.y-Component from Magnitude and Angle: Both use vector magnitude and angle from +x axis.Magnitude of a 2D Vector: Both use vector x component and vector magnitude.Magnitude of a 3D Vector: Both use vector x component and vector magnitude.Unit Vector Component (Normalization): Both use vector x component and vector magnitude.Angle Between Two 2D Vectors (Components): Both use vector x component.
8 more relatedCross Product z-Component of Two 2D Vectors: Both use vector x component.Dot Product of Two 2D Vectors (Components): Both use vector x component.Dot Product of Two 3D Vectors (Components): Both use vector x 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.
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x-Component from Magnitude and Angle explained

θ|v|vx

Resolving a vector is the reverse of building one: the shadow it casts on the x-axis has length |v| cos θ. Simon Stevin demonstrated the underlying parallelogram rule in 1586 with an inclined-plane thought experiment (a closed loop of beads draped over a wedge that would have to move forever if forces did not combine this way) and Newton restated it as Corollary I of the Principia. Every ramp problem since is an application: a 200 N pull on a sled at 25° above the ground drives the sled forward with 200 × cos 25° ≈ 181 N, while the rest of the effort merely lifts.

The classic trap is measuring the angle from the wrong line. The cosine belongs to the component along the axis the angle is measured from; take the angle from the vertical instead and cosine and sine swap places. Check by sanity: at θ = 0° the whole vector lies on x, and cos 0° = 1 delivers exactly that.

x-Component from Magnitude and Angle formula

vx=∣v⃗∣cos⁡θv_x = |\vec{v}| \cos\theta
Where
  • vxv_x= x-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). x-Component from Magnitude and Angle Formula & Calculator. https://formula.expert/solvers/vector-x-component

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