Major and tube radii
Major radius R + Tube radius r
V = 2π²Rr²; S = 4π²Rr
Open calculator ↗GEOMETRY, ONE FIGURE AT A TIMERing torus.
Ring torus.
Understand every measure.
A circle swept around an outside axis. Four free tools, clear formulas and a little discovery along the way.
Find your calculator ↗FIGURE 243D / REFERENCE DRAWING
RING TORUSNOT TO SCALE
THE CALCULATOR DESK
Start with what you know.
4 calculators available
Outer radius and hole radius
Outer radius + Hole radius
R = (outer+hole)/2; r = (outer−hole)/2
Open calculator ↗Surface area and major radius
Surface area S + Major radius R
r = S/(4π²R)
Open calculator ↗Volume and major radius
Volume V + Major radius R
r = √[V/(2π²R)]
Open calculator ↗MEET THE FIGURE
A ring torus, explained.
A ring torus is formed by rotating a circle around a coplanar axis that does not meet it. The major radius R measures from the axis to the tube centre. The tube radius r measures the circular cross-section, with R > r.
Understand the properties ↗LOOK A LITTLE CLOSER
More than a formula.
The volume follows Pappus’s centroid theorem.
Major radius is not outer radius. All tools reject R ≤ r so that the result remains a ring torus.
Explore three geometry facts ↗These tools use ideal Euclidean geometry. Every input must use the same unit. Numerical results are rounded and do not replace measurement, specialist design or safety checks. See worked examples.