Why measure around the pile instead of across it?

Because walking a tape around the toe is a measurement you can actually take, and pacing a diameter is not. To measure a diameter you have to know where the centre is, and the centre of a stockpile is buried under the whole pile — so in practice people sight across it and take a line that misses. Every line that misses the centre is a CHORD rather than a diameter, and a chord is always shorter. That matters more than it sounds, because volume goes with the square of the radius: a diameter read ten per cent short gives a volume nearly twenty per cent short. A circumference has no such failure mode. You walk the visible edge, the tape follows the ground, and the radius comes out of it by division. It is also easier to do alone and easier to repeat.

Why does the material change the answer so much?

Because the height is derived from the material rather than measured, and different materials stand at different angles. Angular crushed stone interlocks — its broken faces catch on each other — so it holds a face around 38 to 45 degrees. Rounded gravel cannot do that; the grains roll, and it settles nearer 30 to 38. Over the same footprint that difference is large: a steeper cone is a taller cone, and volume goes up with height directly. The same effect explains why damp sand stands steeper than dry, which surprises people — a little surface moisture binds grains together and lets the pile hold a face it otherwise could not. Add more water and that reverses sharply, because a saturated material loses the binding and slumps. The angle is genuinely a property of the material AND its condition, which is why the page asks what the pile is made of and reports a band rather than a number.

Is this the volume I should order, or the volume I dug out?

Neither, exactly, and the distinction costs people money regularly. What this gives is LOOSE volume — the material as it sits in the pile, with air between the particles from being tipped. The same material occupied less space in the ground, which is bank volume, and it will occupy less again once it is laid and compacted, which is compacted volume. For most soils and aggregates loose volume is meaningfully larger than bank, and compacted is smaller than bank. So if you are hauling a pile away, this is roughly the number of lorry loads. If you are asking how big the hole was that it came out of, it is not. And if you are asking how much of the pile you need to fill a given space to a specified compaction, it is not that either — that calculation starts from the compacted volume required and works backwards through the same factors.

What if the pile has been driven over?

Then it is a truncated cone rather than a cone, and the page handles that if you give it the width of the flat — but the answer gets less reliable rather than more. A freely tipped pile is a predictable shape because gravity and the material's own angle made it. A pile that has had a loader driven over the top has been shaped by a machine, and how much came off the apex is a guess rather than a measurement. It has usually also been compacted where the tracks ran, so part of the pile is no longer at loose density. The page drops its confidence when you enter a flat for exactly that reason. The honest position is that a levelled pile can be estimated but not measured, and if the number matters — for payment, for a dispute, for reconciliation — the answer is a survey rather than a tape and a formula.

Materials & Quantities

Stockpile Volume Calculator from Base and Angle of Repose

How much is in a stockpile, from the distance round its toe and the material's angle of repose, since its height is the one thing you cannot measure.

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Every formula citedNamed published standards
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Market

Imperial · sales tax

Distance around the toe of the pile

Walk a tape around the bottom edge of the pile.

Circumference rather than diameter, because it is the measurement you can actually take accurately. Pacing a diameter means guessing where the centre is under several metres of material, and any line that misses the centre reads short — which under-states the volume by the square of the error.

Material

What the pile is made of — it sets how steeply it stands.

The material matters more than anything else here, because the height is derived from its angle of repose rather than measured. Angular crushed stone stands markedly steeper than rounded gravel of the same size, so the same footprint holds noticeably more of it.

Width of any flat top

Zero for a freely tipped cone; the diameter of the flat if it has been levelled.

A pile that has been driven over or scraped flat is no longer a cone but a truncated one, and its volume is lower than the cone the same footprint would make. Leave this at zero unless there is a genuine flat on top — a slightly rounded apex is still a cone for these purposes.

Loose volume in the pile

147 yd³

Medium confidence

Between 115.0 and 147.2 yd³, a band 28% wide. Angular faces interlock, which is why crushed stone stands noticeably steeper than gravel. The pile stands 12.19 ft to 15.60 ft tall at those angles, which is the height you could not have measured anyway. This is LOOSE volume: more than the same material occupied in the ground, and more than it will occupy once compacted.

Lower end of the range: 114.98 yd³
Upper end of the range: 147.16 yd³
Width of the range: 27.99 %
Base diameter, from the circumference: 31.19 ft
Derived height, shallowest angle: 12.19 ft
Derived height, steepest angle: 15.6 ft

Then change the inputs to see how far the answer moves.

Show calculation logic

How this was calculated

Formula source(s)

A freely tipped pile forms a cone whose side stands at the material's ANGLE OF REPOSE, so its height is the base radius times the tangent of that angle and its volume is πr²h/3. Measuring the circumference of the toe and deriving the rest is the standard field method, because the apex is the one point on a pile nobody can reach
Angles of repose are quoted as bands rather than values: dry sand roughly 30 to 35 degrees, rounded gravel 30 to 38, angular crushed stone 38 to 45, wood chip 40 to 48. Moisture moves a material within its band, and how the pile was placed moves it again
The result is LOOSE volume — the material as it sits in the pile, bulked. It is neither the bank volume it occupied in the ground nor the compacted volume it will occupy in place, and the three differ by a substantial margin for most materials

Inputs used

Distance around the toe of the pile: 98 ft
Material: Crushed stone or angular aggregate
Width of any flat top: 0 ft

Intermediate steps

Lower end of the range: 114.98 yd³
Upper end of the range: 147.16 yd³
Width of the range: 27.99 %
Base diameter, from the circumference: 31.19 ft
Derived height, shallowest angle: 12.19 ft
Derived height, steepest angle: 15.6 ft

Final result147.16 yd³

Confidence note: Between 115.0 and 147.2 yd³, a band 28% wide. Angular faces interlock, which is why crushed stone stands noticeably steeper than gravel. The pile stands 12.19 ft to 15.60 ft tall at those angles, which is the height you could not have measured anyway. This is LOOSE volume: more than the same material occupied in the ground, and more than it will occupy once compacted.

What this calculation does not cover

The result is LOOSE volume — the material as it sits, bulked. It is not the bank volume it occupied in the ground and not the compacted volume it will occupy once placed, and for most materials those three differ substantially. Which one you want depends on whether you are buying it, hauling it or laying it.
The range is the answer, not a hedge. An angle of repose is a property of the material AND its moisture AND how the pile was built, so it is a band; the volume inherits that band. Reporting a single figure would be inventing a precision the geometry does not have.
A cone assumes the pile was tipped freely onto level ground and left alone. A pile pushed up by a loader, built against a wall, or sitting in a hollow is not a cone and this over- or under-states it depending on which.
The ground under the pile is assumed flat. A pile in a dished bay holds more than its visible shape suggests, and one on a crown holds less; neither is visible from outside.
Nothing here converts volume to mass or to a lorry count. Bulk density varies with the same moisture that moved the angle of repose, so a tonnage taken from this figure carries both uncertainties.
Segregation is invisible to the arithmetic. Tipped material sorts itself as it runs down the cone — the coarsest rolls to the toe — so a sample taken from the bottom of a pile is not representative of what is in it.

Estimated cost — your price

Price per yd³ ($)

This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.

Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.

Sources checked 2026-09-15 · v1.0.0

Regulatory standards & verification citations3

A freely tipped pile forms a cone whose side stands at the material's ANGLE OF REPOSE, so its height is the base radius times the tangent of that angle and its volume is πr²h/3. Measuring the circumference of the toe and deriving the rest is the standard field method, because the apex is the one point on a pile nobody can reach
Angles of repose are quoted as bands rather than values: dry sand roughly 30 to 35 degrees, rounded gravel 30 to 38, angular crushed stone 38 to 45, wood chip 40 to 48. Moisture moves a material within its band, and how the pile was placed moves it again
The result is LOOSE volume — the material as it sits in the pile, bulked. It is neither the bank volume it occupied in the ground nor the compacted volume it will occupy in place, and the three differ by a substantial margin for most materials

Cite this page

Your workspace

Most jobs need more than one number. Add the calculators you need next and they open right here, underneath this one — your figures stay on screen and nothing is lost to a page change.

How to calculate stockpile volume from base and angle of repose in 4 steps

Distance around the toe of the pileWalk a tape around the bottom edge of the pile.
MaterialWhat the pile is made of — it sets how steeply it stands.
Width of any flat topZero for a freely tipped cone; the diameter of the flat if it has been levelled.
Loose volume in the pileThe tool computes the loose volume in the pile from those figures and shows the formula, its sources, and a confidence rating alongside it.

Frequently asked questions

Why measure around the pile instead of across it?: Because walking a tape around the toe is a measurement you can actually take, and pacing a diameter is not. To measure a diameter you have to know where the centre is, and the centre of a stockpile is buried under the whole pile — so in practice people sight across it and take a line that misses. Every line that misses the centre is a CHORD rather than a diameter, and a chord is always shorter. That matters more than it sounds, because volume goes with the square of the radius: a diameter read ten per cent short gives a volume nearly twenty per cent short. A circumference has no such failure mode. You walk the visible edge, the tape follows the ground, and the radius comes out of it by division. It is also easier to do alone and easier to repeat.
Why does the material change the answer so much?: Because the height is derived from the material rather than measured, and different materials stand at different angles. Angular crushed stone interlocks — its broken faces catch on each other — so it holds a face around 38 to 45 degrees. Rounded gravel cannot do that; the grains roll, and it settles nearer 30 to 38. Over the same footprint that difference is large: a steeper cone is a taller cone, and volume goes up with height directly. The same effect explains why damp sand stands steeper than dry, which surprises people — a little surface moisture binds grains together and lets the pile hold a face it otherwise could not. Add more water and that reverses sharply, because a saturated material loses the binding and slumps. The angle is genuinely a property of the material AND its condition, which is why the page asks what the pile is made of and reports a band rather than a number.
Is this the volume I should order, or the volume I dug out?: Neither, exactly, and the distinction costs people money regularly. What this gives is LOOSE volume — the material as it sits in the pile, with air between the particles from being tipped. The same material occupied less space in the ground, which is bank volume, and it will occupy less again once it is laid and compacted, which is compacted volume. For most soils and aggregates loose volume is meaningfully larger than bank, and compacted is smaller than bank. So if you are hauling a pile away, this is roughly the number of lorry loads. If you are asking how big the hole was that it came out of, it is not. And if you are asking how much of the pile you need to fill a given space to a specified compaction, it is not that either — that calculation starts from the compacted volume required and works backwards through the same factors.
What if the pile has been driven over?: Then it is a truncated cone rather than a cone, and the page handles that if you give it the width of the flat — but the answer gets less reliable rather than more. A freely tipped pile is a predictable shape because gravity and the material's own angle made it. A pile that has had a loader driven over the top has been shaped by a machine, and how much came off the apex is a guess rather than a measurement. It has usually also been compacted where the tracks ran, so part of the pile is no longer at loose density. The page drops its confidence when you enter a flat for exactly that reason. The honest position is that a levelled pile can be estimated but not measured, and if the number matters — for payment, for a dispute, for reconciliation — the answer is a survey rather than a tape and a formula.

Preliminary estimate, not certified engineering. This tool produces an indicative quantity calculation for planning purposes only — it is not a certified structural analysis, a guaranteed material takeoff, or a substitute for building department approval. Always verify measurements on-site and have a licensed contractor or structural engineer review any load-bearing, code-sensitive, or safety-critical work before purchasing materials or starting construction. Spotted an arithmetic or standards error? Report it to contact@craftquantities.com with your inputs — a confirmed fix gets a permanent check of its own, so the same mistake cannot come back.