Curve Radius Calculator

1) Why radius matters in construction layout

Curve radius influences alignment, clearances, speed control, and drainage behavior in roads, access paths, rail sidings, and curved walls. A small change in radius can shift offsets at the edge by noticeable amounts, especially over long chords. Using consistent units and reliable measurements helps prevent staking errors that compound between stations.

2) Selecting an input method that matches your notes

Survey and design records rarely provide the same data every time. If you have a measured chord and mid-ordinate, you can reconstruct the circle directly. When drawings report an arc length and central angle, the radius follows from the arc definition. If you are working from a PI with tangents, tangent length with deflection angle gives a practical site solution.

3) Understanding the computed curve elements

The calculator reports arc length, chord, tangent, mid-ordinate, and external distance. These values support setting out PCs and PTs, verifying field offsets, and checking that a curve fits within a right-of-way. External distance is particularly useful to confirm the maximum “bulge” from the tangent intersection toward the curve.

4) Practical checks before issuing results

Keep angles realistic: central angles approaching 180° can magnify small input errors. Confirm mid-ordinate is less than half the chord, and avoid extremely small radii that are difficult to form with typical construction tolerances. Apply rounding consistent with your control network; excessive rounding may hide meaningful differences during verification.

5) Reporting and handover

For approvals and as-built packages, save both the inputs and the computed elements. The CSV export supports quick peer checks in spreadsheets, while the PDF is convenient for daily reports and quality records. Document the chosen method, units, and rounding so another engineer can reproduce the same radius without reinterpreting your field notes again.

1) Which method should I use if I only have a chord measurement?

Use the Chord + Mid-ordinate method if you can also measure the mid-ordinate at the chord midpoint. If you only have a chord, you need either the central angle, arc length, or another curve element to solve the radius.

2) What is a reasonable definition length for degree of curve?

Common arc-definition lengths are 100 ft in imperial work and 30 m in metric work. Use the same definition your project specifications and design team used so your computed radius matches their stated degree of curve.

3) Why does my radius change when I switch methods?

Different inputs carry different field errors. A small mistake in an angle or mid-ordinate can shift the radius noticeably. Verify that all inputs describe the same curve and that units and angle definitions are consistent.

4) Are the computed arc and chord values always the same as my inputs?

For the method you select, the calculator preserves your provided primary values where possible. Other elements are computed from the solved radius and angle, so they may differ slightly due to rounding or because your inputs were approximate.

5) How do I handle very small deflection angles?

Very small angles make tan(Δ/2) close to zero, which can cause unstable results. Increase measurement precision, work in seconds/minutes if available, or use an alternative method such as arc length with central angle.

6) What does external distance represent in the field?

External distance is the maximum offset from the PI toward the curve at the mid-point of the curve’s long chord. It helps check whether the curve will encroach on a boundary or obstacle near the intersection.

7) Can I use the exports for submittals and QA records?

Yes. Save the CSV for independent checking and the PDF for a signed calculation attachment. Include your inputs, units, and rounding selection so reviewers can reproduce the same results during audits.