Rolling sphere protection calculator
A quick, client-side calculator for the protected ground radius around a single vertical mast, using the rolling sphere geometry. Enter the mast height and the sphere radius and read the protected radius. It is an educational estimate to sketch a single rod, not a substitute for a full IEC 62305-3 design.
This calculator estimates the protected ground radius around a single vertical air-termination mast, using the rolling sphere geometry. Give it the height of the mast above the surface it protects and the rolling sphere radius set by your lightning protection level, and it returns the radius of the circle on the ground that the one mast shields. It runs entirely in your browser; nothing is sent anywhere.
The rolling sphere method is one of the three air-termination positioning methods in IEC 62305-3, alongside the mesh method and the protection angle method. This tool takes the simplest case the method allows, one vertical rod on flat ground, and works the geometry for it. For how the three methods work, when each is used and how they combine on a real building, read the full air-termination methods guide. Treat the number here as a sketch to size a single rod, not as a finished design.
Protected radius for one vertical mast
Enter the mast height and the sphere radius. The protected ground radius updates as you type. The sphere radius dropdown offers the commonly cited value for each protection level as a starting point.
Your mast and sphere
How the rolling sphere geometry gives a protected radius
Picture a sphere of a fixed radius resting on flat ground next to a single vertical mast, just touching the tip of the mast. The sphere cannot roll in any closer to the base than the point where it touches both the ground and the mast tip. The circle on the ground directly below that contact, measured out from the foot of the mast, is the part the sphere cannot reach, so it is the part one mast protects. Working out the radius of that circle is pure geometry.
The result is a short formula. With the mast height written as h and the sphere radius as r, the protected ground radius is the square root of h times the quantity two r minus h. The calculator evaluates this each time you change an input. The relationship is not a straight line: a taller mast buys a wider protected circle, but with diminishing return as the height climbs toward the sphere radius, where the protected radius reaches its largest value, equal to r itself.
What this calculator assumes
The number is only as good as the model behind it, so it helps to be clear about what that model takes for granted. Three assumptions matter most.
Where the simple model stops
A single-mast ground radius is a useful first sketch, but a real design needs more than it can give. The rolling sphere is one of three air-termination methods, and on most buildings a designer uses all three together: a mesh across a flat roof, the protection angle to size masts that shield rooftop items, and the rolling sphere to check exposed corners, edges and tall features. The methods guide walks through how they combine.
Three things in particular sit outside this calculator. First, multiple terminations: a building of any size has several rods, masts and conductors whose protected zones interlock, and the full rolling sphere construction is rolled over the whole structure, not applied one rod at a time. Second, structure shape: parapets, plant, antennas, pitched roofs and steps in level all change where the sphere settles, and a flat-ground formula cannot see them. Third, the upper limit: the single-mast geometry holds only while the mast height stays below the sphere radius, and above that the protected zone is governed differently.
From a single rod to the whole system
Sizing one mast is the very start of an air-termination design. The protection level that fixes the sphere radius is itself an output of the Part 2 risk assessment, which decides whether a structure needs protection at all and how strong it must be. From there the lightning protection level sets the sphere radius, the mesh size and the protection angle together, and the full air-termination design places every rod, wire and mesh conductor so no surface a strike could reach is left exposed.