A cutter sets up to drop a 6-inch-deep cut into a slab with a 24-inch diamond blade, marks the line, and assumes the cut stops where the mark stops. It doesn't. At the top surface of the slab, the blade has already chewed past that mark by more than 10 inches on each end. Ask a room full of experienced tradespeople to guess the number before the cut and most land somewhere around two or three inches. The real figure is closer to ten and a half. That gap between the guess and the geometry is where slabs get ruined and pipes get nicked.
The overrun has a few names depending on who you learned the trade from: overcut, run-out, blade overshoot, cut extension. They all describe the same thing, which is the horizontal distance between where the blade reaches full depth and where it first breaks the top surface. The reason the number is so much bigger than intuition expects has nothing to do with blade quality or technique. It's a property of circles, and circles are deceptive at shallow depths.
The blade only touches the work along an arc
A circular blade isn't cutting straight down. It's a disc, and the only part of it doing work at any instant is the segment passing through the material. When you sink that disc 6 inches into a slab, the bottom of the cut sits at full depth, but the blade's edge is curving back up toward the surface on both sides of that low point. Everywhere along that curve, the blade is still in contact with the slab. The point where the arc finally clears the top face is well forward of the line you marked at depth.
This is why the relationship is not intuitive. People mentally model the cut as a rectangle: blade goes down, blade comes across, the cut is as long as the line. The actual shape carved at the surface is governed by a chord of the blade circle, and a chord behaves very differently from a straight drop. Near the bottom of the disc, a small increase in depth moves the contact point a long way horizontally, because the arc is nearly flat there. That flatness is exactly what makes the overrun balloon at shallow cut depths relative to the blade size.
The math is a chord, and the chord is unforgiving early
The closed-form expression is overcut = √(D · (2R − D)), where D is the cut depth and R is the blade radius, half the stamped diameter. It's the same relationship a geometry textbook would call a half-chord length, dressed up in the two numbers a cutter actually has on hand. Run a 24-inch blade (R = 12) at a 6-inch depth and you get √(6 · 18) = √108, about 10.39 inches. Round it the way you'd read a tape and it's 10 7/16 inches of overrun on each side.
The unforgiving part is how the curve front-loads. Cut just one inch deep with that same blade and the overcut is √(1 · 23), about 4.8 inches. So the first inch of depth buys you nearly 5 inches of overrun, while going from 5 inches deep to 6 inches deep adds less than an inch. The overrun grows fastest exactly where most people assume it's negligible. A shallow scoring pass that feels harmless can throw the blade most of a foot past the mark.
| Blade diameter | Cut depth | Overcut per side |
|---|---|---|
| 14 in | 2 in | 4 13/16 in |
| 14 in | 4 in | 6 5/16 in |
| 20 in | 4 in | 8 in |
| 24 in | 6 in | 10 7/16 in |
| 24 in | 10 in | 11 13/16 in |
| 30 in | 6 in | 11 13/16 in |
Read down that table and the pattern is clear: diameter drives the overrun harder than depth does once you're past the first few inches. Bigger blades extend the contact arc, and a larger arc means a longer reach across the surface for the same depth.
There is a hard ceiling, and the formula tells you where
Notice what happens as cut depth climbs toward the radius. At D = R, the blade is buried to its center and the overcut equals R itself, because the chord is now the full diameter at the widest point. You physically cannot cut deeper than the radius in a single pass with a circular blade, since past the centerline the disc starts coming back up out of the material. A 14-inch blade has a 7-inch radius, so 7 inches is the absolute single-pass floor of what that blade can reach, and the overrun at that point is the full 7 inches.
This is the source of the "blade cuts about half its diameter" rule of thumb you'll hear in concrete and masonry circles. It's correct but conservative: nobody runs a blade buried to its exact center, because the overrun there is enormous and the blade is straining. Practical single-pass depth is usually quoted as roughly a third of the diameter, which keeps the overrun manageable and the motor happy. To go deeper, you step the cut in multiple passes, lowering the blade between them.
The angle convention is the other thing that trips people
Tilt the blade for a bevel and the overrun grows, because tilting increases the true depth the blade travels through the material. A slab that's 6 inches thick presents 6 inches of straight-down depth, but tilt the blade 45 degrees and the blade now travels 6 / cos(45°), about 8.5 inches, to get through that same thickness. Feed 8.5 into the chord formula instead of 6 and the overcut on a 24-inch blade jumps from 10 7/16 to roughly 11 1/2 inches.
Here's the trap. There are two conventions for stating a bevel angle, and they're mirror images. Some references measure the tilt from vertical, where 0 degrees is the blade pointing straight down. Others measure from horizontal, where 0 degrees is the blade laid flat. A "45-degree cut" is unambiguous because 45 is 45 either way, but a "20-degree cut" means two completely different blade positions depending on the convention, and the resulting depths and overruns are nowhere near each other. Mixing them up is a classic source of a cut that comes out wrong by an amount that looks plausible until the piece doesn't fit. The only safe practice is to state the reference explicitly every time and, ideally, to look at a drawing of the blade at that angle before committing, because a wrong mental model corrects itself fast when you can see the disc is leaning the opposite way from what you pictured.
Run-out is a clearance problem, not just a length problem
The reason any of this matters on a real job is rarely the length of the cut itself. It's what sits past the line. A countertop cut that overruns by ten inches into open air costs nothing. The same overrun heading toward a wall stud, a buried conduit, a finished edge, or the lip of a pool you're coping costs a repair or a ruined piece of stone. Run-out is fundamentally a clearance question: how much room is there between where the cut needs to stop and the first thing you can't afford to touch.
That reframes the useful calculation. Instead of asking "how far will my blade overrun at this depth," the constraint-driven version asks "given that I have only this much clearance, how deep can I safely cut in one pass." Solving the chord relationship the other direction, D = R − √(R² − O²), where O is the overrun you can tolerate, answers it. With a 24-inch blade and 10 inches of clearance to spare, the deepest safe single-pass cut works out to about 5 3/8 inches. Cut deeper than that and the blade reaches the thing you were trying to avoid. Most geometry tools never frame the problem this way, even though on a job site the clearance is usually the number you actually know and the depth is the number you're trying to find.
What the formula quietly ignores
The chord math treats the blade as a zero-thickness line. Real blades have kerf, the width of material the blade removes, typically an eighth to a quarter inch on large diamond blades. Kerf widens the cut but barely moves the overrun, because the run-out is driven by the radius and depth, not by how wide the slot is. Ignoring it makes the formula slightly conservative, which is the safe direction to err: the tool predicts a hair more overrun than a thin reference cut would show, so following it keeps you on the cautious side of a clearance.
The bigger simplification is that the formula describes ideal geometry, not blade deflection, material chipping, or a blade that wanders off line under load. Those add real-world slop on top of the geometric overrun, never subtract from it. The number the chord gives you is the floor of how far past the line the cut reaches, not a generous estimate. Treat it as the minimum to plan around.
If you cut stone or concrete with a large-diameter blade and want to see this geometry resolve to an actual fractional-inch figure for your blade and depth, including the bevel and clearance-driven versions, Overcut runs the chord math and draws the cut so the overrun stops being a guess.