Search Ctrl K
Home / Tools
THE FEUTEX TOOLKIT

Sphere Cut by a Plane

Find a circular section area and radius for a plane at a given offset from a sphere center.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaSection Radius = sqrt(r**2-d**2); Section Area = PI*(r**2-d**2); Circumference = 2*PI*sqrt(r**2-d**2)
Sources and model references

Made for real tasks

  • Find a circular section area and radius for a plane at a given offset from a sphere center.
Explore step-by-step workflows →

Worked example

Inputs

Sphere radius
5 length
Plane distance from center
3 length

Expected results

Section Radius
4 length
Section Area
50.26548246 length²
Circumference
25.13274123 length

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter sphere radius, plane distance from center.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "r": 5,
  "d": 3
}

Accuracy and scope

Uses finite-precision arithmetic. Results describe the stated mathematical model, not measurement accuracy.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.