Measure ring segment dimensions from angle or height inputs easily. Export clean results for records. Plan annular geometry with fast, dependable calculation support today.
| Outer Radius | Inner Radius | Angle | Ring Segment Area | Outer Arc | Inner Arc |
|---|---|---|---|---|---|
| 12 | 7 | 75° | 16.295878 units² | 15.707963 units | 9.162979 units |
| 20 | 14 | 110° | 79.898994 units² | 38.397244 units | 26.878071 units |
| 9 | 4 | 45° | 5.164395 units² | 7.068583 units | 3.141593 units |
A ring segment is the difference between two circular segments with the same central angle.
Outer segment area: 0.5 × R² × (θ − sin θ)
Inner segment area: 0.5 × r² × (θ − sin θ)
Ring segment area: 0.5 × (R² − r²) × (θ − sin θ)
Outer arc length: R × θ
Inner arc length: r × θ
Chord length: 2 × radius × sin(θ ÷ 2)
Segment height: radius × (1 − cos(θ ÷ 2))
Here, R is outer radius, r is inner radius, and θ is the central angle in radians.
A ring segment is the area between two matching circular segments. It comes from an annulus cut by the same central angle. This shape appears in machining, layout work, duct design, seals, curved plates, and patterned construction. Accurate values help reduce waste. They also improve fit, strength, and planning.
Manual ring segment calculations take several steps. You must work with angle conversion, sector area, triangle area, chord length, and arc length. Small input mistakes can change the final area. This calculator speeds up the process. It gives consistent outputs for outer and inner geometry. It also shows the net annular segment area.
The tool calculates outer segment area, inner segment area, and ring segment area. It also returns outer arc length, inner arc length, chord lengths, segment heights, radial thickness, and mean radius. These values support drafting, estimating, fabrication, and inspection. Engineers and students can compare geometry quickly from one clean results block.
You can use this calculator for gasket design, curved flooring, arch trimming, tank openings, circular channels, and decorative rings. It is also useful in classroom geometry problems. When a drawing shows two radii and one angle, this tool converts the data into practical dimensions that are ready for review.
The calculator supports angle input and outer height input. That makes it flexible when drawings use different dimensions. After submission, the result appears above the form for faster checking. You can then export values to CSV or PDF. This makes reporting easier for worksheets, design notes, and project records.
Ring segment geometry is simple once the relationships are organized well. With accurate formulas and clear validation, you can focus on interpretation instead of repetitive arithmetic. Use the outputs to estimate material, verify sketches, compare design options, and document calculations with confidence.
Because the calculator separates outer and inner segment values, it also helps you audit each step. That is useful for teaching, quality control, and specification sheets. A transparent workflow makes unusual dimensions easier to trust, explain, and reuse in future calculations, templates, and checks later.
A ring segment is the region between two circular segments that share the same central angle. It is cut from an annulus, so it has an outer arc, inner arc, and matching chord geometry.
You can calculate by central angle or by outer segment height. Enter outer radius, inner radius, and your chosen driving value. The calculator then returns the full set of derived measurements.
Use any unit, but stay consistent. If the radii are in millimeters, every length output will be in millimeters and every area output will be in square millimeters.
The shape is based on an annulus. That means the outer circle must be larger than the inner circle. If the inner radius is equal to or greater than the outer radius, the ring segment does not exist.
Yes. Select the angle unit that matches your input. The calculator converts degrees to radians internally before applying the geometric formulas.
Segment height is the perpendicular rise from the chord to the arc. In height mode, the outer segment height is used to recover the shared central angle first.
No. They are optional helpers. Use them when you want a quick CSV file or a simple PDF summary of the current result table.
It is useful for learning, layout checks, and preliminary estimates. For production or safety-critical work, verify assumptions, units, tolerances, and drawing standards before final use.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.