Radial Lot Sizing Calculator
Divide a curved frontage — a cul-de-sac bulb or curved street — into lots with radial side lines. Set the curve once, then size each lot’s central angle to get its arc, chord and area.
Field aid, not a certified plat. Assumes straight radial side lines between a front arc and a concentric rear arc, the common radial-lot layout. Verify against your plat standard before recording.
Curve definition
Lots
| Lot | Angle | Front arc | Front chord | Rear arc | Rear chord | Side | Area |
|---|
How radial lot sizing works
Quick answer: On a curved street, lots are commonly laid out with straight side lines that radiate from the curve’s center point, a front line following the street-side arc, and a rear line following a concentric arc further out. Each lot’s central angle determines its frontage, depth stays constant, and its area follows directly from the two radii and that angle.
Because both the front and rear lines are arcs sharing the same center, each lot is a section of a circular annulus — the ring-shaped area between two concentric circles. Its area is exactly ½ × Δ (radians) × (R2² − R1²), with no approximation needed. This is why equal-angle lots and equal-area lots are the same thing here: area scales directly with angle when every lot shares the same front and rear radii.
Frontage can be described two ways: arc length, the distance measured along the curve, and chord length, the straight-line distance between the same two corners. Chord length is always slightly shorter than arc length, and the gap grows with a larger central angle — worth checking against your local plat standard, since some jurisdictions specify frontage as chord distance and others as arc distance.
Typical use cases
| Situation | Front radius | Rear radius |
|---|---|---|
| Cul-de-sac bulb, lots facing outward | Curb/right-of-way radius | Front radius + lot depth |
| Lots on the inside of a curving street | Larger (street side) | Smaller (interior side) |
Frequently asked questions
Why are the side lot lines radial instead of parallel?
Radial side lines keep every lot’s depth measured consistently from the same center point, which is the standard way to divide a curved street frontage without the side lines converging or diverging awkwardly.
What’s the difference between arc frontage and chord frontage?
Arc frontage is measured along the curve itself; chord frontage is the straight-line distance between the same two corner points. Chord is always a little shorter, and the difference increases with a wider central angle.
Why is equal angle the same as equal area here?
Because every lot shares the same front and rear radii in this layout, each lot’s area is directly proportional to its central angle. If lots had different depths, that would no longer hold.
Can R2 be smaller than R1?
Yes. That represents lots on the inside of a curve, where the rear line is closer to the center than the front line. The area and length formulas work the same way either way.
What if my lot angles don’t add up to the total curve angle?
The calculator shows the remaining, unassigned angle so you can see at a glance whether your lots account for the full curve or leave a gap.
Does this replace a licensed survey or approved plat?
No. This is a design and checking aid. Any lot layout intended for recording should be prepared and certified by a licensed surveyor to your local platting standards.
