The volume of a basin with sloping sides
Cut a rectangular hole with a flat floor L by W and bank the four sides back at a slope of Z horizontal to 1 vertical. At any depth y above the floor, the water surface is (L + 2Zy) by (W + 2Zy). Multiply that out and integrate from zero to h and you get the exact volume:
V = L W h + Z h² (L + W) + (4/3) Z² h³
Three terms, and each one is a shape you can point at. The first is the prism sitting directly on the floor. The second is the four triangular wedges running along the sides. The third is the four corner pyramids where two banks meet. For a 30 by 20 foot floor with 3:1 sides at two feet deep: 1,200 + 600 + 96 = 1,896 cubic feet, about 14,200 gallons.
Note what the terms do as the basin gets deeper. The prism grows linearly with depth, the wedges grow with the square, the corners with the cube. On a shallow wide basin the prism dominates and the side slope hardly matters. On a deep narrow one the slope terms take over, and a change from 3:1 to 4:1 sides moves the volume noticeably — and moves the top opening a great deal more.
The footprint, not the volume, is what runs out
The number people underestimate is not the storage, it is the opening at the top. That same 30 by 20 basin at two feet deep with 3:1 sides has a water surface of 42 by 32 feet. Add a foot of freeboard and the rim is 48 by 38 — 1,824 square feet of lot, three times the floor area, for 1,896 cubic feet of storage.
This is why side slope is the first thing that gets argued about. Steeper sides fit the same volume into a smaller opening, and they are also harder to mow, harder to walk on when wet, harder to climb out of, and more prone to erode. What slope is permitted, and whether a safety bench or a fence is required, is set locally and this page states nothing about it.
| Side slope | Storage at 2 ft on a 30x20 floor | Top opening at 3 ft |
|---|---|---|
| Vertical (0:1) | 1,200 cu ft | 30 x 20 ft |
| 2:1 | 1,643 cu ft | 42 x 32 ft |
| 3:1 | 1,896 cu ft | 48 x 38 ft |
| 4:1 | 2,171 cu ft | 54 x 44 ft |
Going from 2:1 to 4:1 buys 32 percent more storage and costs 77 percent more lot area at the rim. Neither direction is free.
Stage-storage is the useful output, not a single number
A single volume at a single depth answers almost nothing. What a basin design actually runs on is the stage-storage relationship: how many cubic feet are held at every water level from empty to full. That is the curve the routing calculation walks up and down as the storm fills the basin and the outlet drains it, and it is why the calculator lists the volume at every increment rather than only at the top.
The curve is not a straight line. On a basin with sloping sides, the first foot of depth holds far less than the second, because the water surface grows as it rises. On the 30 by 20 basin, the first half foot holds 339 cubic feet and the half foot between 1.5 and 2.0 holds 618, well over half as much again. Anything that assumes storage is proportional to depth is wrong, and wrong in the unhelpful direction near the bottom.
Detention, retention, and what the difference means
A detention basin is dry between storms. It fills, holds water for a while, and lets it out through an outlet at a controlled rate, and the point is to shave the peak of the flow leaving the property rather than to reduce the total. A retention basin holds a permanent pool and only the volume above that pool is available for storm storage — which the arithmetic on this page does not account for, so subtract the permanent pool volume yourself if that is what you have.
The distinction matters for what you are counting. In a retention basin, the storage below the outlet invert is not doing detention work; it is water quality volume, or it is landscaping. In a detention basin, a sediment forebay similarly takes volume out of service.
Why holding the storm volume is not the same as meeting a requirement
The optional section on this page compares the basin storage against a runoff volume, and it is honest arithmetic between two numbers you supplied. It is not a demonstration that the basin works, and it is worth understanding why not.
Detention requirements are almost never written as a volume. They are written as a limit on the peak rate leaving the site, usually for several storm frequencies at once — the post-development peak must not exceed the pre-development peak for the 2-year, the 10-year and the 100-year event, or some local variation on that. Meeting it depends on routing an inflow hydrograph through the basin against the outlet capacity at every stage, and the answer depends as much on the outlet as on the hole.
A basin can hold every drop of the design storm and still fail, if the outlet lets it out faster than permitted. A basin can hold well under the total storm volume and pass, because it was releasing water throughout the event. That routing is engineering work and it is not a calculation to improvise. What this page gives you is the storage side of the input to it, and the outlet and drawdown page gives you the release side.
For the runoff volume itself, the curve number calculator and the rational method flow calculator are the two standard routes, and they answer different questions — volume and rate respectively.
Questions people ask
Why is my basin volume larger than length times width times depth?
Because the sides slope outward, so every layer of water above the floor is wider than the floor. The full expression is L W h + Z h squared times (L + W) + four-thirds Z squared h cubed, where Z is the horizontal run per foot of rise. On a 30 by 20 foot floor two feet deep with 3:1 sides, the floor prism is 1,200 cubic feet, the four side wedges add 600, and the four corner pyramids add 96 — a total of 1,896, which is 58 percent more than the box. Using the box figure understates the storage and, more painfully, badly understates the excavation.
What is the difference between a detention and a retention basin?
A detention basin is dry between storms: it fills, holds the water briefly and releases it through an outlet at a controlled rate, with the goal of reducing the peak flow leaving the site rather than the total volume. A retention basin keeps a permanent pool of water and only the volume above that pool is available for storm storage. The calculator gives the total volume of the excavation shape, so if you have a permanent pool, subtract its volume from the storage you count as available. A sediment forebay takes volume out of service in the same way.
How much freeboard should I allow?
That is set by whoever reviews the design and it is not a number this page will state, because it depends on the size of the basin, whether the embankment is fill or cut, what is downstream of it, and what happens in a storm larger than the design event. The field exists so you can enter your own figure and see the dimensions and earthwork it implies. The general principle is that freeboard is the margin between the design water level and the point at which water leaves in an uncontrolled way over the top of the berm, and overtopping a fill embankment is how small dams fail.
Does holding the whole storm volume mean the basin is big enough?
No, and this is the most common misunderstanding about detention. Requirements are usually written as a limit on the peak flow rate leaving the property, for several storm frequencies at once, not as a volume to store. Whether you meet that depends on routing the inflow through the basin against the outlet capacity at each stage. A basin holding the full storm volume can fail if the outlet releases too quickly, and one holding much less can pass because it was releasing throughout the event. The comparison on this page sets two of your own numbers against each other; it is not a verdict.
Can I build a small detention basin myself?
The excavation of a shallow basin cut into the ground on your own property, well away from structures and property lines, is ordinary earthwork. Three things change that. If any part of it holds water above the surrounding ground behind a raised berm, it is an embankment structure with its own engineering and its own failure mode, and small dams are regulated. If it is anywhere near a foundation, a septic system, a slope or a property line, the siting question is not yours alone to answer. And if the basin exists to satisfy a stormwater requirement, its design has to be one the reviewing authority will accept, which usually means stamped drawings. Call 811 before any of it, and check with the building department first.