Quick answer
Pick 2D or 3D, choose Coordinate or Point per vector, fill fields, tap Calculate angle, read degrees and radians. All processing stays in the browser.
Formula
- θ = arccos((a · b) / (|a| |b|))
- Point mode: v = to - from before dot product
Introduction
Open the Angle Between Two Vectors Calculator and scroll to the island panel under the hero title. That panel is the entire tool: no account, no upload step.
When you need theory behind the readout, read angle between two vectors formula alongside this workflow.
What the calculator does
It builds vector a and vector b from your inputs, computes the dot product and magnitudes, applies arccos, and prints θ in degrees and radians.
Each vector can use Coordinate (components) or Point (from/to displacement) independently.
Nothing is stored on a server: the page is static and the math runs locally after you press Calculate angle.
The tool targets the geometric angle between directions (0° to 180°), matching introductory textbooks rather than signed spin about an axis.
Math the tool runs internally
- Build a, b from inputs
- cos θ = (a · b) / (|a| |b|)
- θ = arccos(clamped cosine)
Errors appear when fields are incomplete or when a vector has zero length. Fix inputs rather than forcing a result.
Input details live in coordinate vs point input for vector angles.
Calculator workflow
- Select 2D or 3D. Applies to both vectors at once.
- Set representation per vector. Coordinate for known components; Point for map or CAD corners.
- Enter all required fields. Missing values block a valid angle.
- Tap Calculate angle. Read degrees, radians, and any error message.
- Cross-check with a hand example. Use worked examples when teaching or grading.
Quick trial
In 2D Coordinate mode, set a = (1, 0) and b = (0, 1). You should see 90° and π/2 radians.
Switch one vector to Point mode with from (0,0) to (3,0) and keep b as (3,4) in coordinates to reproduce the 53.13° triangle.
Toggle to 3D and try a = (1,0,0), b = (0,1,0) to confirm the dimension control before you enter a real z-heavy assignment.
