Vector Calculator

Quick Overview

Use this vector calculator for clear 2D and 3D work. Pick a mode and enter your components. Click an operation and get the result. The tool now lets you switch between 2D and 3D. It supports decimals and negative values. Results appear fast with clean formatting.

How It Works

Inputs

• 2D Vectors or 3D Vectors. Choose the space that fits your problem.
• 2D mode sets z to zero and hides z inputs.
• Cross product appears in 3D mode.
• Vector 1 x. Enter the x component for Vector 1.
• Vector 1 y. Enter the y component for Vector 1.
• Vector 1 z. Enter the z component for Vector 1 in 3D mode.
• Vector 2 x. Enter the x component for Vector 2.
• Vector 2 y. Enter the y component for Vector 2.
• Vector 2 z. Enter the z component for Vector 2 in 3D mode.
• Blank fields count as zero by design.

Operations

• Add. v1 plus v2 returns a vector.
• Subtract. v1 minus v2 returns a vector.
• Dot Product. Returns a single number.
• Cross Product. Works in 3D and returns a vector at right angles.
• Magnitude v1. Returns the length of Vector 1.
• Magnitude v2. Returns the length of Vector 2.
• Normalize v1. Returns a unit vector for v1.
• Normalize v2. Returns a unit vector for v2.
• Angle Between Vectors. Returns degrees and radians.
• Scalar Projection. Returns the length of v1 along v2.
• Clear All. Resets inputs and clears the result box.

Output and formatting

• Vector results show as (x, y) in 2D and (x, y, z) in 3D.
• Scalar results show as a single number.
• Numbers round to four decimals when needed.
• Angle shows both degrees and radians.
• Zero length cases show a clear notice in the result box.

How to Use This Tool

1. Choose 2D Vectors or 3D Vectors.
2. Enter Vector 1 values in the x, y, and z inputs.
3. Enter Vector 2 values in the x, y, and z inputs.
4. Pick one operation and click the matching button.
5. Read the result in the box below the buttons.
6. Click Clear All to start fresh at any time.

Why Use This Vector Calculator?

This vector calculator handles the work that slows you down. It keeps your focus on the problem, not on busy math steps. Use it for class, lab, or quick checks at work.

• Switch between 2D and 3D to match the task.
• Get instant results for common vector math.
• Rounding stays steady to four decimal places.
• Clear labels guide each step.
• Great for physics, graphics, and engineering work.
• Perfect for fast validation before you write the final answer.

Putting It All Together

Limits and notes

• Cross product works in 3D mode only.
• Angle needs both vectors with nonzero length.
• Normalize needs a vector with nonzero length.
• Scalar projection needs Vector 2 with nonzero length.
• Blank inputs count as zero to speed entry.
• 2D mode sets all z values to zero automatically.
• Results round to four decimals for decimal values.
• Clear All removes all inputs and the last result.

Examples of common use

• 2D addition. Choose 2D. Set v1x to 3 and v1y to 4. Set v2x to -1 and v2y to 2. Click Add. Result is (2, 6).
• 3D dot product. Choose 3D. Set v1x to 1 and v1y to 2. Set v1z to 3. Set v2x to 4 and v2y to -5. Set v2z to 6. Click Dot Product. Result is 12.
• 3D cross product. Choose 3D. Set v1x to 1 and v1y to 0. Set v1z to 0. Set v2x to 0 and v2y to 1. Set v2z to 0. Click Cross Product. Result is (0, 0, 1).
• Angle between axes. Choose 2D. Set v1x to 1 and v1y to 0. Set v2x to 0 and v2y to 1. Click Angle Between Vectors. Result shows 90 degrees and about 1.5708 radians.
• Scalar projection. Choose 3D. Set v1x to 3 and v1y to 4. Set v1z to 0. Set v2x to 1 and v2y to 0. Set v2z to 0. Click Scalar Projection. Result is 3.
• Normalize a vector. Choose 2D. Set v1x to 3 and v1y to 4. Click Normalize v1. Result is about (0.6, 0.8).

The vector calculator gives fast answers with clear steps. Use it to check work, explore ideas, and save time on routine math.