Radial Length Calculator

Plotly Graph

The chart draws the solved circle and one radius line.

Example Data Table

Method	Given Inputs	Calculated Radial Length	Unit
From Diameter	Diameter = 120	60	mm
From Circumference	Circumference = 314.159	50	mm
From Area	Area = 7853.982	50	mm
From Arc and Angle	Arc = 78.540, Angle = 90°	50	mm
From Chord and Angle	Chord = 70.711, Angle = 90°	50	mm
From Sagitta and Chord	Sagitta = 13.397, Chord = 70.711	50	mm

Formula Used

1) From diameter: r = d / 2

2) From circumference: r = C / (2π)

3) From area: r = √(A / π)

4) From arc length and angle: r = s / θ, where θ is in radians.

5) From chord and angle: r = c / (2 sin(θ/2))

6) From sagitta and chord: r = c² / (8h) + h / 2

These formulas are common in geometry, machine design, piping layouts, wheel calculations, arc fitting, and curved component inspection.

How to Use This Calculator

Select the engineering method that matches your known inputs.
Enter the measurement unit you want displayed.
Provide the required values for the selected method.
Click the calculate button to solve the radial length.
Review radius, diameter, circumference, area, and any angle-based outputs.
Use the CSV or PDF buttons to export your result summary.
Check the Plotly graph to visually verify the solved geometry.

Frequently Asked Questions

1) What does radial length mean here?

Here, radial length means the radius of a circle or arc. It is the distance from the center point to the circular edge.

2) Which input method is best for engineering work?

Use the method that matches your measured data. Diameter is fastest. Chord with angle or sagitta is useful for field inspection and curved parts.

3) Why must angle-based formulas use radians internally?

Arc formulas use radians because the standard relation is arc length equals radius multiplied by angle in radians. The calculator converts degrees automatically.

4) Can I use inches, meters, or millimeters?

Yes. The calculator does not force a unit. Enter your preferred unit label, and keep all related inputs in the same unit system.

5) When should I use sagitta and chord?

Use sagitta and chord when you can measure the arc rise and span directly. This method is common in fabrication, inspection, and reverse geometry checks.

6) Does the calculator also show diameter and area?

Yes. After solving radial length, it also reports diameter, circumference, and area. Some methods also show arc and chord values for the entered angle.

7) Why do invalid values produce errors?

Some geometric combinations are impossible. Negative values, zero lengths, or invalid angles can break the formulas, so validation helps preserve meaningful output.

8) Is this useful for pipes, gears, and curved plates?

Yes. It helps with circular profiles in piping, wheel design, plate rolling, flange work, machining, layout planning, and inspection calculations.

Advanced Radial Length Calculator

Calculator Inputs