Torus Volume Calculator
Volume, surface area and diameters of a torus from the ring radius and the tube radius.
Results
Volume
394.7842
m³
Surface area
394.7842
m²
Outside diameter
14.0000
m
Inside diameter
6.0000
m
Length of the centre line
31.4159
m
Cross-section of the tube
12.5664
m²
Volume
394,784.176
L
What shape it is
A ring — there is a hole
What this tool does
A torus is a circle swept around an axis, and the neat consequence is that its volume is the tube's cross-section times the distance its centre travels — the same trick that gives the volume of any swept shape. The page also names the shape: when the tube is fatter than the ring there is no hole left, and it stops being a doughnut.
Formula
V = 2π² R r² · A = 4π² R r
Variables
| Symbol | Meaning | Unit |
|---|---|---|
rr | Ring radius, centre to tube centre | m |
r | Tube radius | m |
V | Volume | m³ |
A | Surface area | m² |
OD | Outside diameter | m |
ID | Inside diameter | m |
CL | Length of the centre line | m |
CS | Cross-section of the tube | m² |
LI | Volume | L |
SH | What shape it is | — |
Worked example
- Ring radius, centre to tube centre5 m
- Tube radius2 m
- Volume394.7842 m³
- Surface area394.7842 m²
- Outside diameter14.0000 m
- Inside diameter6.0000 m
- Length of the centre line31.4159 m
- Cross-section of the tube12.5664 m²
- Volume394,784.176 L
- What shape it isA ring — there is a hole
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.