An average depth is the least useful number about an arena
Take twenty probe readings off a working arena and they will not cluster. The track carries almost all the traffic, so it is where the footing gets pushed out to the rail, ground down and dragged thin. The quarter lines and the centre of a jumping arena get a fraction of that. Readings of two and a quarter inches on the track and four and three quarters at the centre average out to something that looks acceptable and describes no part of the surface.
The example loaded into the form above averages 3.49 inches against a four inch target. Read only the average and the arena is about half an inch short, which sounds like a modest top-up. Read the distribution and nine of the twenty readings are at or below three inches while ten are at four or above, and the nine low ones are all the same part of the arena.
Two different jobs, and the identity between them
The output separates them deliberately, because they are not the same purchase.
| Approach | What it buys | On the defaults above |
|---|---|---|
| Uniform lift | Area times the shortfall in the average | 31.6 cu yd, 46.1 tons |
| Fill only what reads short | The share of area below target, by its own average deficit | 40.1 cu yd, 58.5 tons |
| Material already above target | Nothing — it is on the arena already | 8.5 cu yd |
Those three rows are not independent, and the relationship runs against intuition, so it is worth stating plainly. Filling only the low spots always costs more material than lifting the whole surface, and it costs more by exactly the volume already sitting above target: 31.6 plus 8.5 is 40.1. The reason is arithmetic rather than accidental. The average is short only by the net of the deficits and the surpluses, so a uniform lift quietly counts the deep areas as though they helped, which they do not. Spread material evenly and the low spots come up by the average shortfall rather than by what they are actually missing, and they stay proportionally low.
Which leaves the third row, which is not a purchase at all. When the average is at or above the target and a third of the readings are still short, there is more material above target on that arena than the low spots are missing, and moving it is a grading job rather than a delivery.
Standard deviation, in tons
The spread figure is printed twice: once in inches and once as the tonnage that one standard deviation of depth represents across the whole surface. On the 200 by 100 ft example at 100 lb per cubic foot, a standard deviation of 0.86 inches is about 77 tons of material — the quantity that separates a consistent surface from an inconsistent one, expressed as something you could put on a truck. It is a useful way to see whether the arena has a material problem or a grading problem before deciding which one to pay for.
Taking readings that mean something
A probe, a length of rod, or a long screwdriver pushed down until it hits the base. The two failure modes are both about where you stand. Sampling only the middle of the arena, because it is easier to walk, produces a survey that says the arena is deep. Sampling only the track, because that is where the problem obviously is, produces one that says it is empty. Neither describes the surface.
A grid does. Pace out a regular pattern — the track at both long sides, the quarter lines, the centre line, and a few points across the short ends — and take the same pattern each time so successive surveys compare. Note the pattern down somewhere. Twenty readings on a grid is worth more than a hundred taken wherever the probe happened to be.
A caution about the base: a probe stops where it meets resistance, which is the top of the base only if the base is firm. On a soft or contaminated base the probe keeps going and the reading overstates the footing. If the readings are wildly deeper than the material delivered can account for, that is worth investigating as a base problem rather than recorded as a deep spot.
Where the numbers go next
Once you have a tonnage, the arena footing calculator handles the ordering side — density, settlement allowance, loads and the cost of a depth change — and it is the page to use when you are choosing a depth rather than measuring one. If the survey has turned up standing water or a track that keeps thinning in the same place, the problem may be under the footing rather than in it, and the arena base and crown calculator covers the base course and the fall across the surface. For what the footing weighs when wet, and the water a moisture change takes, the arena footing water calculator works from the same volume.
Questions people ask
How many depth readings should I take?
Enough to cover the parts of the arena that behave differently, which usually means at least fifteen to twenty on a regular grid rather than a handful in convenient places. The important thing is the pattern, not the count: readings must include the track at both long sides, the quarter lines, the centre and the short ends, because those are the places that differ. Twenty on a grid tells you more than sixty taken wherever you happened to walk, and repeating the same pattern later lets two surveys be compared instead of just averaged.
The average meets my target but parts of the arena are thin. What now?
That is the redistribution case, and the page names it separately for a reason. If the average is at or above target, the arena already holds the material it needs and the material is in the wrong places. The output prints the cubic yards sitting above target alongside the cubic yards the short areas are missing, and when the first is larger than the second, grading moves it for the cost of machine time rather than the cost of a delivery. Buying material and spreading it evenly leaves the same distribution with more in it.
Why does the calculator give two different tonnages, and why is the smaller job the bigger number?
Because the two jobs are not the same purchase. A uniform lift multiplies the whole area by the shortfall in the average, which buys material for every square foot including the parts already at depth. Filling only what reads short multiplies the share of readings below target by their own average deficit. The second is always the larger of the two, by exactly the volume already sitting above target, because the average is short only by the net of the deficits and the surpluses — a uniform lift counts the deep areas as though they compensated for the thin ones, which on the ground they do not. On the defaults that is 46.1 tons against 58.5, a difference of 8.5 cubic yards that is already on the arena.
What depth should my footing be?
Not something this page answers, which is why the target is a field. Footing depth depends on the material and its gradation, the discipline the arena is used for, the base underneath and the horses working on it, and the people who can advise are the footing supplier and whoever built or maintains the arena. This calculator takes the target you were given and reports how far the surface is from it, where, and what closing the gap costs in tons. It has no opinion about the target itself.
Can I use this for a round pen or an irregular arena?
For a round pen, put the equivalent area in as a length and width whose product matches the circle: a 60 ft pen is 2,827 sq ft, so 60 by 47.1 ft gives the same area and every volume comes out right. For an irregular shape, do the same with any pair of dimensions that multiply to the real area. The statistics on the readings do not depend on the shape at all, only on the sample being spread evenly across whatever the surface is, so the average, range and spread stay valid regardless.