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Vector Components Calculator

Work out vector components instantly with clear inputs, formula shown and shareable results.

About Vector Components Calculator

Resolving a vector splits it into perpendicular components. In the plane that is simply x = r·cos θ and y = r·sin θ; adding an elevation angle scales the horizontal part by cos φ and gives z = r·sin φ.

Formula

Components

x = r·cos φ·cos θ, y = r·cos φ·sin θ, z = r·sin φ

Worked example

With the default values below, Vector Components Calculator returns x component of 34.640970. Change any input above and every figure here is recalculated in your browser.

Inputs used

Magnitudeminimum 0
50
Angle from the x-axis
36.87 °
Elevation above the xy-planeaccepts -90–90 °
30 °

Results

x component
34.640970
y component
25.980824
z component
25.000000
Recomputed magnitude
50.000000

Step by step

  1. 1Values used
  2. 2Components
  3. 3x component= 34.640970
  4. 4y component= 25.980824
  5. 5z component= 25.000000
  6. 6Recomputed magnitude= 50.000000

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

A magnitude of 50 at 36.87° with zero elevation?

x = 40 and y = 30 — the 3-4-5 triangle scaled by ten. Adding elevation shrinks both by a factor of cos φ and lifts the rest into z.

Why does the magnitude come back unchanged?

Because the components are perpendicular, Pythagoras in three dimensions recovers the original length exactly.

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