Measure circle angles from multiple linked geometric inputs. Compare arc, chord, and sector relationships instantly. Save results, tables, and graphs for simpler revision later.
Circle angle work usually starts with radians because arc and sector formulas are direct in that form.
The calculator returns the minor angle first. Major angle values are also displayed for comparison and checking.
| Method | Radius | Source Input | Minor Central Angle | Minor Arc Length | Minor Sector Area |
|---|---|---|---|---|---|
| Arc and radius | 10 | Arc = 15.707963 | 90° | 15.707963 | 78.539816 |
| Sector and radius | 12 | Area = 75.398224 | 60° | 12.566371 | 75.398224 |
| Chord and radius | 8 | Chord = 8 | 60° | 8.37758 | 33.510322 |
| Angle and radius | 6 | Angle = 135° | 135° | 14.137167 | 42.411501 |
Circle angle measurement connects geometry, trigonometry, and graphical reasoning. A central angle starts at the center, while an inscribed angle starts on the circle itself. Both describe the same intercepted arc, but they do not have the same size.
When radius and arc length are known, the central angle comes directly from the radian definition. When radius and sector area are known, the area formula gives the angle. When radius and chord are known, inverse sine is the useful path.
This page also reports major and minor values. That helps when checking whether your figure uses the shorter arc or the longer arc. Students often calculate a correct minor angle but forget to compare it with the major companion.
The graph supports visual verification. It plots the circle, then highlights the minor arc and the matching chord. That makes the relationship between algebraic output and geometric shape easier to inspect before using the result in classwork, assignments, or exam revision.
The chord method returns the minor central angle. A single chord usually matches the shorter arc first. Subtract that result from 360° to get the major central angle.
Yes. Enter diameter when radius is unknown. The calculator converts diameter into radius automatically and then uses the same circle formulas.
Radians make arc length and sector area formulas direct. Once the radian angle is found, the calculator also converts it into degrees for easier reading.
A central angle equals its intercepted arc measure. An inscribed angle intercepting the same arc is always half of that measure.
Use arc length mode when you know the radius and the length of the arc. It is one of the fastest ways to recover a central angle.
Yes. Compare your manual angle, arc, sector, and chord values with the result table. The graph also helps confirm whether the geometry looks reasonable.
In intercepted arc modes, the graph can use a unit circle when no radius is entered. That keeps the angle picture visible for checking relationships.
It shows how much of the full circle the minor angle covers. For example, 90° covers one quarter, so the percentage becomes 25%.
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.