The catch point is an intersection, not a division
Ask someone how far out a 2 to 1 cut slope runs from a hinge that is three feet below the ground and they will say six feet. That is right only if the ground is dead level. The design slope is climbing away from the hinge at one foot up for every two out, and the ground is usually doing something of its own — climbing, falling, or both across the same section. The catch point is where those two lines meet, and the distance depends on the difference between their slopes, not on either one alone.
Written out: for a cut, the distance out from the hinge is the depth divided by the design slope rate minus the ground slope rate. For a fill, the ground is working with you rather than against you on rising ground, so the two rates add. With a 3.2 foot cut on a 2 to 1 slope, level ground gives 6.40 feet. Ground rising at 8 percent gives 7.62 feet, about 19 percent further out. Ground falling at 8 percent pulls it in to 5.52 feet. Same depth, same slope, three different stakes.
When there is no catch at all
If the ground rises faster than the cut slope climbs, the two lines diverge and never meet. If the ground falls faster than the fill slope drops, the same thing happens on the other side. The arithmetic returns a negative or infinite distance, which on the ground means the section does not close: the cut runs into the hillside forever, or the fill toe never lands. There is no staking answer to that. It is a wall, a bench, a flatter slope or a different alignment, and it is a design decision.
Watch for it in the input as well as the output. A 4 to 1 cut slope is climbing at 25 percent. On ground that climbs at 30 percent it will never daylight, and that is not a rare hillside.
The end area falls out of the same triangle
| Quantity | How it comes out | Example: 3.2 ft cut, 2 to 1, 8% ground |
|---|---|---|
| Distance out | Depth divided by (slope rate minus ground rate) | 3.20 / (0.500 − 0.080) = 7.62 ft |
| Catch elevation | Hinge elevation plus distance over the slope ratio | 100.00 + 7.62/2 = 103.81 ft |
| End area, this side | Half the hinge depth times the distance out | 0.5 × 3.20 × 7.62 = 12.19 sq ft |
| Face length | Distance out times the slope length factor | 7.62 × 1.118 = 8.52 ft |
The gap between the ground and the design slope is the full hinge depth at the hinge and zero at the catch, and it closes in a straight line between them, so the area is a triangle. That is the side-slope part of a cross section; add the part under the finished surface itself and you have the end area that goes into a volume. The average end area calculator takes those areas station by station and turns them into yards.
What the section does not tell you
One section describes one station. Between two staked sections the ground is assumed to run straight, and it usually does not. On a curve the two sides of the section are not mirror images and the offsets differ. Rock, groundwater or a soft layer changes what slope the material will stand at and none of that appears in the geometry. And the elevations feeding the whole thing came from somewhere — see the levelling loop calculator for how they get established and checked, and the grade stake calculator for the finished-surface stakes inside the hinge points.
Questions people ask
What exactly is the hinge point?
The line where the finished surface stops and the side slope starts — the edge of the shoulder, the edge of the pad, the outer edge of subgrade, depending on what is being built. Everything on this page is measured from it: the design elevation is the elevation at the hinge, the cut or fill depth is the difference between ground and design there, and the catch distance is measured out from it. If your drawings dimension the side slope from the centreline instead, enter the hinge offset so the output gives you centreline offsets as well.
Why is the catch point further out than depth times the slope ratio?
Because that shortcut assumes the ground is level, and a cut slope climbing at 1 in 2 against ground that is also climbing only closes the gap at the difference between the two rates. Take a 3.2 foot cut on a 2 to 1 slope: level ground gives 6.40 feet, ground rising at 8 percent gives 7.62 feet. On ground that falls away, the effect reverses and the catch comes in closer. The steeper the natural cross slope, the bigger the error in the level-ground shortcut.
What side slope should I use?
Whatever the design specifies. What a cut face or an embankment will stand at depends on the material, how wet it is, how high the slope is and what is above and below it, and that is a geotechnical and design question rather than something to pick from a table. This page runs out the ratio you enter and has no opinion about whether it is right for your soil. A slope built steeper than the material will hold does not sag first as a warning; it goes all at once.
Where does the stake actually go?
Practice varies, and it is worth agreeing on before the crew starts. Some set a stake at the catch itself and accept losing it. Some set it at a fixed offset beyond the catch and mark the distance back in plus the height difference, so it survives the first pass and the catch can be re-established from it. The offset field here gives you both numbers. What matters more than the choice is that every stake on the job uses the same one and says so on the face.
Can I use this for a trench or a basement excavation?
The geometry is the same — a face running out from a hinge until it meets existing ground — so the offsets and the end area apply. What does not carry over is anything about safety. The slope, benching or shoring that keeps an excavation from collapsing is governed by rules and by a competent person on site assessing the actual soil, not by a daylight calculation. Excavation walls fail without warning and a cubic yard of soil weighs more than a small car. Run the geometry here; get the excavation itself designed and inspected by whoever is qualified to do it.