Rolling Sphere Method Calculator: IEC, NFPA, AS

This rolling sphere method calculator estimates the protected radius around a single vertical mast, using the sphere radius IEC 62305-3, NFPA 780 or AS 1768 sets.

Give it the height of the mast above the surface it protects and the rolling sphere radius for your standard, and it returns the radius of the circle the one mast shields. It works in metres or feet and runs entirely in your browser; nothing is sent anywhere.

The rolling sphere method appears in all three standards. IEC 62305-3:2024 lists it beside the mesh and protection angle methods. NFPA 780-2026 lists it beside the angle method and air terminal placement rules. AS 1768:2021 builds its Appendix D around it. This tool takes the simplest case, one vertical rod on flat ground, and works the geometry for it. For how the methods combine on a real building, read the air-termination methods guide, the NFPA 780 zone of protection guide or the AS 1768 air terminal placement guide.

The calculator

Protected radius for one vertical mast

Choose metres or feet, enter the mast height and pick a sphere radius preset from your standard. The protected radius updates as you type, and the line under the result says which clause the radius comes from.

Your mast and sphere

MetresFeet

Mast height above the protected surface

m

tip height, not total length

Rolling sphere radius

m

Sphere radius preset

IEC 62305-3, class of LPS I

IEC 62305-3, class of LPS II

IEC 62305-3, class of LPS III

IEC 62305-3, class of LPS IV

NFPA 780, largest striking distance: 150 ft (45 m)

NFPA 780, explosives, flammable vapors, watercraft: 100 ft (30 m)

AS 1768, LPL I

AS 1768, LPL II

AS 1768, LPL III

AS 1768, LPL IV

AS 1768, LPL I, large flat surface

AS 1768, LPL II, large flat surface

AS 1768, LPL III, large flat surface

AS 1768, LPL IV, large flat surface

each value is read from the standard named

The IEC radii come from IEC 62305-3:2024 Table 2, the AS radii from AS 1768:2021 Table D.1, and the NFPA striking distances from NFPA 780-2026 Sections 4.7.3.1.4, 7.3.2, 8.2.1 and 10.3.1.1. The formula 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

Pick a preset to fill the radius from a standard.

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. AS 1768:2021 prints it as Equation D.3.3(1). NFPA 780-2026 Section 4.7.3.3 prints a version for two heights, an upper and a lower roof, which becomes the same formula when the lower height is the earth. IEC 62305-3:2024 prints no formula for this case, but the geometry behind its Clause 5.2.2.2 is the same. A taller mast buys a wider protected circle, 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 stands for the striking distance of a lightning flash. All three standards tie it to the peak current of the flash with the same relation: IEC 62305-3:2024 Clause D.5.2.2.2, NFPA 780-2026 Section B.3.2.2 and AS 1768:2021 Equation D.3.1. A smaller sphere also catches the weaker flashes, so it is the stricter choice, and it gives a smaller protected radius for the same mast. Change the radius in the tool and watch the protected radius move with it.

The radius by standard

Which sphere radius each standard sets

The three standards agree on the geometry and differ on what picks the radius. IEC and AS tie it to a protection level that the risk assessment produces. NFPA 780 ties it to the kind of structure.

Standard	How the radius is set	What picks it	Where it is set
IEC 62305-3:2024	One radius for each class of LPS, smallest for Class I	The class of LPS, which matches the lightning protection level one for one (Table 1)	Table 2; method in Clause 5.2.2.2
NFPA 780-2026	No more than 150 ft (45 m)	The type of structure (Section 4.7.3.1)	Section 4.7.3.1.4
NFPA 780-2026	100 ft (30 m)	Structures housing explosives, and watercraft	Sections 8.2.1 and 10.3.1.1
NFPA 780-2026	100 ft (30 m) or less	Structures holding flammable vapors or gases	Section 7.3.2
AS 1768:2021	One radius for each LPL, smallest for LPL I	The LPL from the Section 2 risk assessment (Clause D.2), applied along the edges	Table D.1; Equation D.3.3(1)
AS 1768:2021	Twice the standard radius of the same LPL	The doubled radius for large flat surfaces (Clause D.3.2)	Table D.1; Equation D.3.3(2)

IEC 62305-3:2024

Clause 5.2.2.1 calls the rolling sphere the general method that suits every case, with the protection angle as a supplement for simple shapes. Table 2 sets the radius by class of LPS, and Table 1 matches each class to the protection level from the IEC 62305-2 risk assessment. Read more in the protection levels guide.

NFPA 780-2026

Section 4.7.3.1 sizes the sphere by the type of structure, and Section 4.7.3.1.4 caps it at 150 ft (45 m). Section 8.2.1 uses 100 ft (30 m) for structures housing explosives, and Section 10.3.1.1 the same for watercraft. The NFPA 780 zone of protection guide covers the angle method too.

AS 1768:2021

Clause D.3.2 sets three steps: rods on points and corners, the standard sphere along edges, then the doubled sphere across large flat surfaces. Clause D.2 notes most ordinary structures that need protection end up at LPL III. The AS 1768 air terminal placement guide works the steps through.

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 standard sets for your protection level or structure type. Each preset names the table or section it comes from. Check it against your own copy of the standard before you rely on a design.

The limits

Where the simple model stops

A single-mast radius is a useful first sketch, but a real design needs more than it can give. On most buildings a designer combines placement methods: under IEC 62305-3 a mesh across a flat roof, the protection angle for masts over rooftop items and the rolling sphere for corners and edges; under AS 1768 the three steps of Clause D.3.2; under NFPA 780 the angle method and air terminal spacing beside the sphere. 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 a sketch that shows how mast height and sphere radius drive the protected zone for one rod. A full design covers the whole structure, combines the methods your standard allows, and is worked to its precise values. Lumex^™ is independent of IEC, NFPA and Standards Australia; buy the standard from its publisher for design and certification.

Where this sits

From a single rod to the whole system

Sizing one mast is the very start of an air-termination design. Under IEC 62305 the protection level that fixes the sphere radius is an output of the Part 2 risk assessment, and the lightning protection level then sets the sphere radius, the mesh size and the protection angle together. AS 1768:2021 works the same way, with its LPL coming from the Section 2 assessment. NFPA 780 is different: its risk assessment, Annex L, is informative and guides the decision on whether to protect, and the striking distance follows from the type of structure.

Size the rod here, but get the need for protection from the assessment.

Lumex^™ runs the risk assessment of IEC 62305-2:2024, NFPA 780-2026 Annex L and AS 1768:2021, shows the working behind every figure and recommends the protection measures. Under IEC and AS that includes the protection level your design must meet. Drawing the air-termination layout and signing it stays with a competent person. See

how Lumex^™ runs NFPA 780

and

how Lumex^™ runs AS 1768

, or run an assessment.

FAQs

Questions answered

What is the rolling sphere method?

The rolling sphere method places air terminals by rolling an imaginary sphere of a fixed radius over and around a structure from every direction. Any surface the sphere touches could be struck, so terminals are placed until the sphere rests only on them. All three main standards use it: IEC 62305-3:2024 Clause 5.2.2.2, NFPA 780-2026 Section 4.7.3 and AS 1768:2021 Clause D.3. This calculator applies the geometry to the simplest case, one vertical mast on flat ground.

What sphere radius should I use?

Use the radius your standard sets. IEC 62305-3:2024 Table 2 sets it by the class of LPS, and AS 1768:2021 Table D.1 by the protection level, plus a doubled radius for large flat surfaces. In both, the stricter the level, the smaller the sphere. NFPA 780-2026 caps the striking distance at 150 ft (45 m) in Section 4.7.3.1.4 and uses 100 ft (30 m) for explosives in Section 8.2.1. Each preset in the calculator fills the radius for the level or structure you pick and names the table or section it comes from.

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 rolling sphere geometry. It is the radius of the circle the sphere cannot reach because the mast holds it off. The real protected volume is three-dimensional and curves inward with height, so this ground figure is one 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 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 type.

What formula does this calculator use?

It uses r = the square root of h times (2R minus h), where h is the mast height and R is the sphere radius. AS 1768:2021 prints this as Equation D.3.3(1). NFPA 780-2026 Section 4.7.3.3 prints a two-height version that reduces to it when the lower height is earth. IEC 62305-3:2024 sets the method and the radius but prints no such formula; the geometry is the same. It holds while h stays below R.

Can I enter heights in feet?

Yes. The unit switch changes the calculator between metres and feet and converts the values already entered, at 0.3048 m to the foot. NFPA 780-2026 prints its distances in feet with metres in brackets, so an NFPA preset shows 150 ft or 45 m exactly as printed rather than converting one into the other. The IEC and AS radii are printed in metres only, so their feet values are converted in code.

Why does AS 1768 use a doubled sphere on flat roofs?

AS 1768:2021 Clause D.3.2 notes that the plain rolling sphere is conservative on large flat roofs, which are struck less often than corners and edges. So it uses the standard radius for edges, and a radius twice as large for large flat surfaces, listed beside it in Table D.1. Equation D.3.3(2) then gives the protected distance along the roof. Pick an increased radius preset and the calculator labels its result as a distance along the flat surface.

What happens when the mast height reaches the sphere radius?

The single-mast formula holds only while the mast height stays below the sphere radius. At that point the protected radius reaches its largest value, equal to the radius itself. NFPA 780-2026 Section 4.7.3.3.2 likewise limits its formula to a height difference no greater than the striking distance. For a taller mast the full rolling sphere construction is needed, so the calculator flags the case and shows the limiting value instead of extending the formula.

Does this replace a real lightning protection design?

No. This is a sketching aid for one vertical mast on flat ground. A real design covers the whole structure, usually combines the rolling sphere with other placement methods, accounts for parapets, plant and roof shape, and is worked to the standard you are designing to. The standards are sold by IEC, NFPA and Standards Australia, and you need your own copy for design and certification.

What Lumex^™ does, and what stays with you

Lumex^™ computes the method of the standard you choose, IEC 62305-2:2024, AS 1768:2021 or NFPA 780-2026, 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 R_T = 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. The standard's introduction then lets national or local regulations fix R_T, the tolerable frequency of damage F_T, and the Annex A, B, C and E calculation rules and parameter values. Every IEC 62305-2 assessment in Lumex^™ states the jurisdiction it was computed under and the values that applied.

Rolling sphere method calculator