Free tool

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.

An engineer working through an electrical diagram beside a control panel

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.

The calculator

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

tip height, not total length
LPL I, 20 m LPL II, 30 m LPL III, 45 m LPL IV, 60 m
commonly cited values, confirm against the standard
The four radii are widely published convenience values, not a reproduced IEC table. Confirm the exact radius for your lightning protection level against IEC 62305-3 before you rely on a design. The formula used is the square root of h times two r minus h, valid while h is less than r.
Protected ground radius
0.00 m
protected circle around the mast base
Protected diameter
0.00 m
Ground area covered
0.00 m²
Enter a mast height below the sphere radius to get a protected radius.
What it does

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.

Why the sphere radius drives everything. The radius represents the striking distance of a lightning flash, and it is fixed by the lightning protection level your risk assessment arrived at. A more demanding level uses a smaller sphere, which gives a smaller protected radius for the same mast, which is the same reason a more demanding level needs more or taller terminations. Change the radius in the tool and watch the protected radius move with it.
Assumptions

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.

A single vertical mast

The geometry is for one upright rod or mast. Real layouts use several terminations whose protected zones overlap, and the combined cover is not the sum of single-mast circles. This tool sizes one rod, on its own.

Flat, level ground

The protected radius is measured on a flat surface at the base of the mast. A pitched roof, a parapet, a step in level or nearby tall objects all change what the sphere can reach, and none of them are in this simple model.

A radius set by the standard

The sphere radius is the one your protection level dictates. The dropdown gives the commonly cited value for each level as a convenience; the exact figure for a design comes from IEC 62305-3 for the level you are working to.

The limits

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.

An estimate, not a design. Treat the protected radius here as an educational estimate that shows how mast height and sphere radius drive the protected zone for one rod. It is not a substitute for a full IEC 62305-3 design, which covers the whole structure, combines the three methods, and is worked to the precise values the standard sets for your protection level.
Where this sits

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.

Size the rod here, but get the class from the assessment. The sphere radius you use is fixed by the lightning protection level, and the level comes out of the Part 2 risk assessment. Lumex computes that assessment and reports the level your design must meet. Drawing the Part 3 layout and signing it stays with a competent person. When you are ready, run an assessment.
FAQ

Questions answered

What is the rolling sphere method?

The rolling sphere method is one of the three ways IEC 62305-3 lets you position air terminations. You take a sphere of a fixed radius and roll it over and around a structure from every direction. Wherever the sphere touches a surface, a lightning strike could attach there, so air terminations are placed so the sphere rests only on them and never on a part of the building you need to protect. The radius is fixed by the lightning protection level: a more demanding level uses a smaller sphere. This calculator applies the geometry to the simplest case, a single vertical mast on flat ground.

What sphere radius should I use?

The rolling sphere radius is set by the lightning protection level chosen in your risk assessment, with the most demanding level using the smallest sphere. The four levels, LPL I to IV, are commonly cited with radii of 20, 30, 45 and 60 metres. Those four figures are widely published, but you should confirm the exact value for your level against IEC 62305-3 itself before relying on a design. The calculator offers them as a convenience in the dropdown, not as a reproduced copy of the standard.

What does the protected radius mean?

The protected radius is the distance out from the base of the mast, on flat ground, within which the ground is shielded by that single mast under the rolling sphere geometry. It is the radius of the circle on the ground that the rolling sphere cannot reach because the mast holds it off. Anything inside that circle, at ground level, is inside the protected zone of that one mast. The real protected volume is three-dimensional and curves inward with height, so this ground figure is a simple slice through it, useful for sizing but not the whole picture.

Why does the mast height matter?

Height decides how far the sphere is held off the ground. A taller mast lifts the sphere higher, so the circle it cannot reach on the ground grows wider, up to the point where the mast height equals the sphere radius. The relationship is not linear: the protected radius is the square root of the height times twice the radius minus the height. Doubling the height does not double the protected radius. The calculator works this out live as you change the height.

What formula does this calculator use?

It uses the standard rolling sphere geometry for a single vertical rod on flat ground: the protected radius equals the square root of h times the quantity two r minus h, where h is the mast height above the protected surface and r is the rolling sphere radius. This comes straight from the geometry of a circle of radius r resting on the ground and touching the tip of a mast of height h. It is ordinary mathematics, not text taken from the standard, and it is valid while the height stays below the sphere radius.

Does this replace a real IEC 62305-3 design?

No. This is an educational estimate for one vertical mast on flat ground. A real lightning protection design covers the whole structure, usually combines the rolling sphere with the mesh and protection angle methods, accounts for the actual shape of the building and its rooftop features, and is worked to the precise values in the standard for the chosen protection level. Use this tool to get a feel for how mast height and sphere radius drive the protected zone, then carry the work into a full Part 3 design.

How does the protected radius relate to the protection level?

The protection level sets the sphere radius, and the sphere radius feeds straight into the protected radius. A more demanding level, LPL I being the most demanding, uses a smaller sphere, which gives a smaller protected radius for the same mast height. So a single mast covers a smaller footprint at a more demanding level, which is the same reason such levels need more or taller terminations. Change the radius in the calculator to see the protected radius move with it.

What happens when the mast height reaches the sphere radius?

The simple single-mast formula is valid while the mast height stays below the sphere radius. At the point where the height equals the radius, the protected radius reaches its maximum, equal to the radius itself, and the simple ground-radius geometry no longer applies the same way above that. For a mast taller than the sphere radius the protected zone is governed differently and the full rolling sphere construction is needed, so the calculator flags the case and treats the value as the limiting one rather than extending the formula past where it holds.

Is this calculator based on copyrighted IEC tables?

No. The geometry formula is standard mathematics. The four sphere radii in the dropdown are values that are commonly cited across the industry and presented here as a convenience, with a clear note to confirm them against IEC 62305-3. The tool does not reproduce any IEC table, figure or clause text. For the exact figures and the full method you should read the standard itself, which this page cites by number rather than copying.
What Lumex does, and what stays with you

Lumex computes the IEC 62305-2 method and shows the working. It does not certify a structure. You may not issue or submit a Lumex output until a competent person, qualified where the structure is located, has reviewed the inputs and the result and signed it.

The tolerable risk in IEC 62305-2 is not a fixed constant. Clause 7.3 NOTE 1 gives RT = 1×10-5 per year as a representative value of tolerable risk and adds that another value may be set once the case has been investigated in detail. Printed p.12 then lets national or local regulations fix RT, the tolerable frequency of damage FT, and the Annex A, B, C and E calculation rules and parameter values. Every Lumex assessment states the jurisdiction it was computed under and the values that applied.

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