Vector Converter: Convert Cartesian, Cylindrical, and Spherical

Use this vector converter to switch between coordinate systems fast. Convert Cartesian and Cylindrical and Spherical values with clear steps. All angles use radians. A helpful diagram shows each system and its axes.

What Does the Vector Converter Do?

The tool converts a point or position vector between systems. Pick your input type and enter your values. Pick the output type and click Convert Vector. Results appear with four decimal places. Angles show in radians, and a degrees line appears for Cylindrical and Spherical outputs.

Angle names follow common physics use. Theta is the azimuth in the xy plane. Phi is the polar angle from the positive z axis. Typical ranges are theta from negative pi to pi and phi from 0 to pi.

How to Use This Tool

Step 1: Pick Your Input Format

Open the Convert from menu and choose Cartesian or Cylindrical or Spherical. You will see fields for that system.

Step 2: Enter Your Data

Fill in numbers for each field. Use radians for angles.

• Cartesian x y z Enter three numbers that describe your point.
• Cylindrical r theta z Set r zero or positive. Set theta in radians from the x axis. Set z as height along the z axis.
• Spherical r theta phi Set r zero or positive. Set theta as azimuth in radians. Set phi as polar angle in radians from the positive z axis.

To convert degrees to radians, use degrees times pi divided by 180.

Step 3: Choose the Output Format and Convert

Open the Convert to menu and choose the target system. Click Convert Vector to compute your result.

• Cartesian output Shows x then y then z.
• Cylindrical output Shows r and theta in radians and z.
• Spherical output Shows r and theta in radians and phi in radians.
• Degrees line Lists theta or phi in degrees for quick reference.

Why Use This Tool?

This vector converter saves time and reduces errors from manual steps. Angle units stay clear on every run. The diagram helps you check axis labels and angle names. Related vector and geometry links now match your task.

• Formulas at a glance Cartesian to Cylindrical. r equals sqrt of x squared plus y squared. theta equals atan2 of y and x. z stays z.
• Cartesian to Spherical. r equals sqrt of x squared plus y squared plus z squared. theta equals atan2 of y and x. phi equals arccos of z over r when r is above zero.
• Cylindrical to Cartesian. x equals r cos theta. y equals r sin theta. z stays z.
• Spherical to Cartesian. x equals r sin phi cos theta. y equals r sin phi sin theta. z equals r cos phi.

Final Thoughts

Keep these notes in mind for best results.

• Enter a number in every field.
• Radial distance r stays zero or positive.
• The zero vector sets phi to 0 in Spherical output.
• Theta uses atan2 so values can span negative pi to pi.
• Results round to four decimals for display.
• To enter degrees, multiply by pi divided by 180.
• Use this tool for position coordinates and point conversions.

Common use cases include these tasks.

• Physics with circular or spherical symmetry.
• 3D graphics and camera placement.
• Robotics arm target points in space.
• Engineering models that switch between systems.
• Homework checks and quick study.

Quick examples for clarity.

• Cylindrical to Cartesian Input r equals 5. Theta equals 90 degrees. z equals 2. Convert degrees with 90 times pi divided by 180. Result x equals 0. y equals 5. z equals 2.
• Spherical to Cartesian Input r equals 3. Theta equals 0.785 rad. Phi equals 1.047 rad. Result x about 1.8371. y about 1.8371. z about 1.5000.
• Cartesian to Spherical Input x equals 2. y equals 2. z equals 1. Result r equals 3.0000. theta about 0.7854 rad. phi about 1.2310 rad. Degrees line shows 45.00 degrees and 70.53 degrees.

Use the vector converter whenever you need clean, consistent coordinate changes. It keeps your math tidy and your focus on the work.