Advanced Vector Polar Coordinate Calculator

Convert, analyze, compare, and visualize vectors across coordinate systems with precise steps, flexible angle settings, advanced operations, exports, and interactive graphing tools for everyone.

Calculated result

Vector analysis

Calculation steps


    

Calculator settings

Cartesian vector input

Polar vector input

Initial and terminal points

Advanced vector operations

Cylindrical coordinate conversion

For Cartesian input, the second field is y. The angle setting applies only to cylindrical angles.

Spherical coordinate conversion

The spherical polar angle φ is measured from the positive z-axis.

Complex number and phasor conversion

Multiple-vector batch input

Use commas between values. Blank lines are ignored.

Output options

Interactive vector graph

Inspect components, angles, origins, endpoints, and resultants.

Calculation history

Formula used

Magnitude: r = √(x² + y²)
Direction: θ = atan2(y, x)
Cartesian components: x = r cos(θ), y = r sin(θ)
Unit vector: v̂ = v / ‖v‖
Dot product: A · B = AₓBₓ + AᵧBᵧ
Projection: projᵦ(A) = ((A · B) / ‖B‖²)B
Cylindrical: x = ρ cos θ, y = ρ sin θ, z = z
Spherical: x = r sin φ cos θ, y = r sin φ sin θ, z = r cos φ

How to use this calculator

Select a mode and enter the required vector values. Choose angle units, direction, range, and precision before calculating. Results appear above the form with detailed calculation steps.

Use the graph controls to inspect vector direction and components. Export the result as CSV, PDF, copied text, or an image. Saved calculations remain available in your browser history.

Example data

Mode Input Expected result
Cartesian to polar x = 3, y = 4 r = 5, θ ≈ 53.130102°
Polar to Cartesian r = 10, θ = 30° x ≈ 8.660254, y = 5
Two points (1, 2) to (6, 8) v = ⟨5, 6⟩, r ≈ 7.81025
Dot product A = ⟨3,4⟩, B = ⟨−2,5⟩ A · B = 14

Frequently asked questions

What is a polar vector?

A polar vector uses magnitude and direction. It represents the same vector as Cartesian components.

Why does this calculator use atan2?

The atan2 function preserves quadrant information. It also handles vertical vectors more reliably.

Can the angle be negative?

Yes. Choose the signed range option. Negative angles follow your selected rotation direction.

What happens with a zero vector?

Its magnitude is zero. Its direction and unit vector remain undefined.

Can I use radians or gradians?

Yes. Select your preferred angle unit. All displayed angles follow that setting.

How are compass bearings handled?

Compass bearings begin at north. They increase clockwise under standard bearing conventions.

Does a negative magnitude work?

Yes. The calculator converts it to positive magnitude. It also rotates direction by half a turn.

Can I calculate several vectors together?

Yes. Use batch mode for multiple lines. The calculator also reports their resultant vector.

Are my history entries uploaded?

No. History stays inside local browser storage. Clearing browser data can remove it.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.