What does Fits inside mean here?

The object radius is smaller than the usable inradius after tolerance. Positive margin means there is space left before touching a face.

When is a fit considered tight?

A fit is tight when the margin is positive but close to the tolerance range. That is a warning to review manufacturing error, coating, and measurement precision.

How do I use reverse mode?

Enter the object radius you need to fit. The required edge output gives the minimum regular tetrahedron edge after tolerance allowance.

geometry calculator

Tetrahedron Sphere Fit Checker

When you need to know whether a spherical insert, clearance envelope, sensor body, bead, or rounded part fits inside a regular tetrahedron.

Fit-check tool for engineers, CAD users, and students asking whether a sphere-like object fits inside a regular tetrahedron.

Fit Check + Reverse Sizing

Will the Object Fit Inside the Tetrahedron?

Enter the edge, object radius, and tolerance. Use reverse sizing when you know the object first.

The inradius is the largest sphere radius that can touch all four faces from inside.

Tetrahedron Edge Length(units)

Outer edge length of the regular tetrahedron.

Object Radius to Fit(units)

Radius of the sphere or rounded object you want to place inside.

Tetrahedron Sphere Fit Checker Output

Enter values to see the result.

Why This Fit Check Matters

If the object is too large

It will not physically fit inside the tetrahedron.
Tolerance errors increase the failure rate.
Assembly may require force, sanding, or redesign.

If the object is much smaller

You may waste internal space.
The part may sit loosely or shift during assembly.
A smaller tetrahedron might meet the same fit requirement.

How Tight Is the Fit?

Tolerance Risks Before You Approve the Fit

Comparing object radius to raw inradius while ignoring tolerance.

Using object diameter in the radius field.

Treating a tiny positive margin as safe when the manufacturing process has larger error than the margin.

Fit Logic Behind the Decision

usable radius = edge x sqrt(6) / 12 - tolerance; margin = usable radius - object radius

A regular tetrahedron can contain a centered sphere up to its inradius. For real parts, subtract tolerance before comparing that capacity with the object radius.

Reverse edge = (target object radius + tolerance) x 12 / sqrt(6).

Edge to Capacity Table

This table uses your current object radius and tolerance to show which edge sizes would pass.

Edge	Max object radius	Margin for your object	Decision
2.50	0.5103	0.5003	Fits
3.00	0.6124	0.6024	Fits
4.00	0.8165	0.8065	Fits
5.00	1.0206	1.0106	Fits
6.00	1.2247	1.2147	Fits

Next Step Depends on the Fit Result

If the object does not fit, increase edge length first and compare the redesign with Percentage Increase Calculator.

If the object fits but vertex clearance matters too, check the bounding sphere in Regular Tetrahedron Circumradius Calculator.

If you need material volume after the fit is approved, continue with Regular Tetrahedron Volume Calculator.

If coating or surface coverage becomes the next constraint, calculate it in Regular Tetrahedron Surface Area Calculator.

If the fit margin must be turned into a percent safety buffer, use Percentage Calculator.

If the part changes from a tetrahedron to a prism enclosure, move the fit review to Right Triangular Prism Surface Area Calculator.

Next Tetrahedron Sphere Fit Checker Moves

Next Calc

Important Use Notice

Informational calculator only. Verify important outputs independently before legal, tax, medical, engineering, safety-critical, contractual, employment, or compliance use.