Analyze split rings from radii and gap angle. See remaining area, removed section, and arcs. Built for quick checks, examples, exports, and accurate learning.
| Case | Input Type | Outer | Inner | Gap Angle | Remaining Area | Remaining Outer Arc |
|---|---|---|---|---|---|---|
| Example 1 | Radii | 10.00 | 6.00 | 30.00° | 184.3068 | 57.5959 |
| Example 2 | Radii | 14.00 | 9.00 | 60.00° | 301.0693 | 73.3038 |
| Example 3 | Diameters | 24.00 | 12.00 | 45.00° | 296.8805 | 65.9734 |
1. Outer radius and inner radius: If diameters are entered, divide each diameter by 2.
2. Ring thickness: Thickness = Outer Radius − Inner Radius.
3. Mean radius: Mean Radius = (Outer Radius + Inner Radius) ÷ 2.
4. Full annulus area: Area = π(Outer Radius² − Inner Radius²).
5. Removed gap area: Removed Area = (Gap Angle ÷ 360) × Full Annulus Area.
6. Remaining split ring area: Remaining Area = Full Annulus Area − Removed Gap Area.
7. Circumference and arc lengths: Circumference = 2πr. Remaining Arc = Full Arc × (1 − Gap Angle ÷ 360).
8. Area ratio: Retained % = (Remaining Area ÷ Full Annulus Area) × 100.
A split ring is often modeled as an annulus with an open sector cut from it. That simple geometry appears in many class problems. It also appears in design sketches and quick layout work. This calculator helps you move from raw dimensions to usable results without repeating the same manual steps. It takes an outer size, an inner size, and a gap angle. Then it returns the most useful measures in one place.
You can enter values as radii or diameters. That makes the page easier to use with different worksheets and notes. After conversion, the calculator finds ring thickness and mean radius. It also computes the full annulus area before the gap is removed. Next, it calculates the area lost to the gap sector. Finally, it shows the remaining split ring area. Those outputs support geometry practice, checking, and comparison.
Area alone is not always enough. Many users also need arc lengths. This page therefore reports the full outer and inner circumferences. It also shows the remaining arcs after the gap is removed. Gap arc lengths are listed too. These values help you understand how much of the circular boundary still remains. They also make ratio checks easier. If the gap is one sixth of a full turn, one sixth of the area and arc length should be removed.
That relationship is important in geometry. It connects annulus formulas with sector formulas. When you see both parts together, the shape becomes easier to understand. The example table on this page adds another layer of clarity. It lets you compare different input sets quickly. The export tools are also practical. You can save your results for homework notes, worksheets, or simple reports.
Use this calculator when you want faster checks and fewer arithmetic mistakes. It is useful for tutoring, self-study, revision, and prototyping. It is also useful when dimensions change often. Instead of recomputing each formula by hand, you can adjust inputs and recalculate. The page stays simple. Enter values, calculate, read the results, and export them if needed. That clean flow supports accurate and repeatable maths work.
This calculator treats a split ring as an annulus with a sector gap removed. It is a ring shape with an opening defined by a gap angle.
Yes. Choose the diameter option in the input type field. The calculator converts diameters to radii before using the formulas.
A ring needs an outside boundary and an inside boundary. If the outer value is not larger, the geometry is invalid and the annulus area cannot be formed correctly.
If the gap angle reaches 360 degrees, the whole ring is removed. A valid split ring must keep some remaining arc and some remaining area.
Length results use the unit label you enter. Area results use the square of that label, such as cm², mm², or in².
Yes. The current version uses degrees for the gap angle. If you have radians, convert them to degrees before entering the value.
It is the share of the full annulus that remains after the sector gap is removed. It helps compare different split ring openings quickly.
The mean radius is useful for centerline estimates, comparisons, and quick checks. It also helps when you want a representative radius between the inner and outer edges.
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.