Torus Volume Calculator
Example Data Table
Use this table to understand common torus calculations.
| Major Radius | Minor Radius | Unit | Angle | Approx Volume |
|---|---|---|---|---|
| 10 | 3 | cm | 360° | 1776.53 cm³ |
| 5 | 1.5 | m | 180° | 111.03 m³ |
| 8 | 2 | in | 270° | 473.74 in³ |
| 12 | 4 | ft | 360° | 3789.12 ft³ |
Formula Used
The calculator uses the standard torus volume equation:
V = 2π²Rr²
Here, R is the major radius. It measures the distance from the torus center to the center of the tube.
r is the minor radius. It measures the radius of the circular tube.
For a partial torus, the volume becomes:
Vpartial = 2π²Rr² × angle / 360
The curved surface area is:
A = 4π²Rr × angle / 360
If end caps are selected for a partial torus, this calculator adds 2πr².
Estimated mass is calculated as:
Mass = Volume in m³ × Density × Quantity
How To Use This Calculator
- Enter the major radius of the torus.
- Enter the minor radius of the tube.
- Select the length unit used by your measurements.
- Use 360 degrees for a full torus.
- Use a smaller angle for a partial torus segment.
- Enter density if you want an estimated mass.
- Select the desired decimal precision.
- Press the calculate button to view results.
- Download the result as CSV or PDF when needed.
Understanding Torus Volume In Physics
What A Torus Represents
A torus is a ring shaped solid. It looks like a tire, washer, doughnut, or magnetic coil. In physics, this shape appears in fluid flow, plasma rings, electric coils, and rotating mechanical parts. Its volume tells how much space the solid body occupies.
Why The Two Radii Matter
A torus needs two radii. The major radius defines the distance from the center of the whole ring to the center of the tube. The minor radius defines the tube thickness. A small change in minor radius can greatly change volume. This happens because the minor radius is squared in the formula.
Practical Physics Uses
This calculator helps with density, mass, buoyancy, and material planning. Engineers can estimate the amount of material in a circular gasket. Students can compare volume changes during geometry experiments. Designers can test ring shaped parts before production.
Partial Torus Calculations
Many real parts are not complete rings. They may be curved pipe sections, arc magnets, or partial seals. The angle input handles these cases. A full torus uses 360 degrees. A half torus uses 180 degrees. A quarter torus uses 90 degrees.
Surface Area And Mass
Volume alone is not always enough. Surface area helps when studying coating, heat transfer, paint coverage, or friction. Mass is useful when density is known. The calculator converts volume to cubic meters for this mass step. This keeps the physics calculation consistent.
Better Measurement Practice
Measure both radii carefully. Use the same unit for both values. Do not confuse diameter with radius. If you have a diameter, divide it by two first. For precise work, use more decimal places. For classroom estimates, two or three decimals are often enough.
FAQs
1. What is a torus?
A torus is a ring shaped solid formed by rotating a circle around an axis outside the circle. Common examples include tires, washers, rings, and doughnuts.
2. What is the major radius?
The major radius is the distance from the center of the whole torus to the center of the circular tube.
3. What is the minor radius?
The minor radius is the radius of the tube that forms the torus. It controls tube thickness and strongly affects volume.
4. What formula calculates torus volume?
The standard formula is V = 2π²Rr². R is the major radius, and r is the minor radius.
5. Can this calculate a partial torus?
Yes. Enter an arc angle below 360 degrees. The calculator multiplies the full torus volume by the angle fraction.
6. Why is density included?
Density lets the calculator estimate mass. It converts volume to cubic meters, then multiplies by density and quantity.
7. Should I enter radius or diameter?
Enter radius values only. If you have diameter values, divide them by two before using the calculator.
8. What does surface to volume ratio mean?
It compares exposed surface area with enclosed volume. It helps in heat transfer, coating, fluid contact, and material studies.