Hexagonal Plate Weight & Custom-Shape Calculations

Hexagonal plate weight comes from the same area, volume, mass chain as any other plate, with the hexagon area worked out from the across-flats dimension: A = 0.8660 × AF². Irregular custom plates do not have a single formula, so they get split into shapes you can measure or taken straight from CAD. Either way the area then goes into the Steel Plate Weight Calculator under Other shape, which accepts a face area directly.

That last point is worth stating plainly up front. The calculator has geometries for rectangles, discs, rings and triangles, but no hexagon button. For a hexagon or anything more complicated, you work out the area yourself and enter it. This article is about getting that area right.

What makes a hexagon regular

A regular hexagon has six equal sides and six equal internal angles of 120 degrees. That regularity is what lets one dimension describe the whole shape.

If the six sides are not equal, none of the formulas below apply, and the plate belongs in the custom-shape section further down. Plenty of parts described as hexagonal on a drawing are not regular hexagons, so check the side lengths before reaching for a shortcut.

The formula for hexagonal plate weight

A regular hexagon can be described by across-flats, across-corners, or side length. All three give the same area, but each has its own constant:

Dimension you have	Area formula	Constant
Across flats (AF)	A = (√3 ÷ 2) × AF²	0.8660
Across corners (AC)	A = (3√3 ÷ 8) × AC²	0.6495
Side length (s)	A = (3√3 ÷ 2) × s²	2.5981

• AF is the distance between two opposite parallel faces, measured square across
• AC is the distance between two opposite corners, which is the longer measurement
• s is the length of one of the six sides

The relationships between them are fixed: AC = AF × 1.1547, and AF = s × 1.7321. Once the area is settled, the rest is the usual chain:

V = A × t
m = V × ρ

Across flats and across corners are not the same number

This is where hexagon calculations fail. Across corners is 15.47% longer than across flats on every regular hexagon, so mixing them up puts a 15% error straight into a squared term.

The size of the mistake is fixed, which at least makes it recognisable. Using the across-flats constant on an across-corners measurement gives an answer 33.3% too heavy. The other way round gives one exactly 25% too light.

Calipers naturally land on the flats. Drawings frequently dimension across corners, particularly where the plate has to fit a bore or clear a fixture. Confirm which one you are holding before squaring it.

Worked example: a 300 mm hexagon

A hexagonal blank, 300 mm across flats, 8 mm thick, in mild steel at 7.85 g/cm³.

1. Work in one unit. AF = 30 cm, t = 0.8 cm
2. Face area. A = 0.8660 × 30² = 0.8660 × 900 = 779.42 cm²
3. Volume. V = 779.42 × 0.8 = 623.54 cm³
4. Mass. m = 623.54 × 7.85 = 4,895 g = 4.89 kg

Had that 300 mm been an across-corners dimension instead, the area would be 0.6495 × 900 = 584.57 cm² and the mass 3.67 kg. Same drawing note, same number typed, 25% less steel.

A quick sanity check on any hexagon: it always covers 86.6% of the square that its across-flats dimension would make. The 300 mm hexagon sits inside a 300 mm square of 900 cm², and 779.42 is 86.6% of that.

The same hexagon in imperial

Nothing changes but the density figure. A 12 inch across-flats hexagon, 1/2 inch thick, in mild steel at 0.2836 lb/in³:

1. Face area. A = 0.8660 × 12² = 124.71 in²
2. Volume. V = 124.71 × 0.5 = 62.35 in³
3. Weight. m = 62.35 × 0.2836 = 17.7 lb

The three constants in the table are pure geometry, so they hold in any unit system. Only the density has to match the units you are working in.

A small measuring error costs twice as much

Because area depends on AF squared, a percentage error in the measurement roughly doubles by the time it reaches the weight. Get the dimension 1% wrong and the answer is about 2% wrong.

Measure the 300 mm hexagon as 302 mm and the area becomes 0.8660 × 30.2² = 789.85 cm² instead of 779.42, which is 1.34% heavy off a 0.67% measuring error.

That is not a reason to chase decimal places on a transport estimate. It is a reason to measure across the flats carefully when the figure is going into a costing, and to prefer a drawing dimension over a caliper reading on a cut edge where the flame or plasma cut has left the face slightly out of square.

The same doubling applies to every squared term in this cluster: disc diameters, ring diameters and hexagon dimensions all behave this way. Linear dimensions like plate thickness do not, which is why a thickness tolerance moves the answer proportionally rather than doubly.

Check the hexagon against the calculator

The hexagon area goes in through the Other shape geometry, which takes a face area rather than dimensions.

1. Open the Steel Plate Weight Calculator.
2. Set Blank geometry to Other shape.
3. Enter Face area 779.42 and set that field’s unit to cm².
4. Enter Thickness 8 mm.
5. Select Mild Steel ASTM A36.

Success test: the result should be about 4.89 kg, matching the hand calculation. If it does not, the usual causes are an area unit left on mm² or m² rather than cm², or the across-corners constant used on an across-flats measurement.

That Other shape field is the general-purpose route for this whole article. Anything whose area you can establish, by formula, by decomposition or by CAD, can be weighed this way.

Irregular and custom profiles

There is no formula for an arbitrary plate profile, and any page offering one is describing a specific shape rather than a general method. What there is instead is a procedure.

Split the profile into shapes you can measure

Most fabricated profiles resolve into rectangles, triangles, circles and parts of circles. Work out each piece, add the material, subtract the voids.

Take a bracket plate: a 600 × 400 mm rectangle with a 250 × 150 mm notch cut from one corner and two 60 mm diameter holes.

1. Base rectangle. 60 × 40 = 2,400 cm²
2. Subtract the notch. 25 × 15 = 375 cm²
3. Subtract the holes. 2 × π × 3² = 56.55 cm²
4. Net face area. 2,400 − 375 − 56.55 = 1,968.45 cm²
5. At 12 mm thick in mild steel. 1,968.45 × 1.2 × 7.85 = 18,543 g = 18.54 kg

Enter 1,968.45 cm² and 12 mm into the calculator under Other shape and you get the same figure.

Two habits make this reliable. Write down every piece as you go, including the ones you subtract, so the working can be checked. And decide up front whether small features are in or out, rather than including some and forgetting others.

Curved edges and part circles

A rounded corner is a quarter circle. A slot end is a half circle. A curved edge that follows an arc can usually be treated as a segment of a circle, added or subtracted like anything else.

Where the curve does not resolve into a recognisable piece of a circle, the decomposition approach has reached its limit. That is the signal to get an area from CAD rather than push the estimate further.

Take the area from CAD when you have it

Any drawing produced in a CAD system already knows its own area, and most nesting software reports it per part. That figure is better than a hand decomposition because it accounts for every fillet, chamfer and cut-out exactly.

Copy it into the Other shape field with the matching unit and the estimate is as good as the drawing. This is the shortest path for complex parts, and it removes the decomposition step entirely.

When to stop calculating by hand

Hand decomposition is worth it for a handful of parts with a few features each. It stops being worth it in two situations.

The first is complexity: once a profile has a dozen features, the chance of missing one is higher than the accuracy you gain. The second is volume: forty parts across three thicknesses is a spreadsheet job or a CAD job, not a hand job, because transcription errors outnumber arithmetic errors at that scale.

Neither is a limitation of the maths. Both are about where errors actually come from.

Where hexagon and custom estimates go wrong

Assuming an irregular hexagon is regular. Six sides does not mean six equal sides. Measure two or three before trusting a single dimension to describe the shape.

Using the enclosing rectangle. The envelope of a shaped plate is always heavier than the plate. For a hexagon the gap is 13.4%, and for a heavily cut profile it can be far more. The envelope is still the right number for what you buy, so keep the two figures separate rather than picking one.

Forgetting that holes are voids. Every hole subtracts, and on a plate with many of them the total matters. Two 60 mm holes in the bracket above removed 0.53 kg.

Nominal against actual. All of this works from drawing dimensions and a reference density. Thickness tolerance, cutting tolerance and grade variation are not in the arithmetic, so a calculated figure stays an estimate. Weigh the part where an exact number is required, and never treat a weight as evidence that a plate is strong enough for its job.

Changing material without rechecking. Density is the only input that is not geometry. The 300 mm hexagon is 4.89 kg in mild steel and 1.68 kg in aluminium 6061, a difference large enough to change how it gets handled. The aluminium plate weight guide covers what the alloy does to that figure.

Hexagon and custom profile FAQs

What is the formula for the weight of a hexagonal plate? Work out the area with A = 0.8660 × AF² where AF is the across-flats dimension, then multiply by thickness and material density. If your drawing gives across corners, use 0.6495 × AC² instead.

What is the difference between across flats and across corners? Across flats is measured between two opposite parallel faces; across corners is measured between two opposite points. Across corners is 15.47% longer on every regular hexagon.

How do I calculate the weight of an irregular steel plate? Split it into rectangles, triangles and circles, add the material areas, subtract the voids, then multiply the net area by thickness and density. If the part came from CAD, use the reported area instead.

Can the calculator handle a shape that is not one of its geometries? Yes. Select Other shape and enter the face area directly, which covers hexagons, irregular profiles and anything taken from nesting software.

Do I need to subtract small holes? It depends what the number is for. Ignore them for a transport estimate; subtract them for costing a batch or for any calculation running close to a limit.

Area first, everything else follows

Every shape in this cluster reduces to the same question: what is the face area? Rectangles, discs, rings and triangles each have a formula that answers it. Hexagons have three, depending on which dimension you were given. Custom profiles have a procedure instead of a formula.

Once you have the area, put it into the Steel Plate Weight Calculator under Other shape along with your thickness and material, and compare it against your own working before trusting it on the rest of the job.