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Reviewed by Bogna Szyk and Jack Bowater Last updated: Mar 11, 2022 Have you ever wondered how to find the central angle of a circle? The central angle calculator is here to help; the only variables you need are the arc length and the radius. Read on to learn the definition of a central angle and how to use the central angle formula. What is a central angle?A central angle is an angle with a vertex at the centre of a circle whose arms extend to the circumference. You can imagine the central angle being at the tip of a pizza slice in a large circular pizza. You can find the central angle of a circle using the formula:
where θ is the central angle in radians, L is the arc length and r is the radius. Where does the central angle formula come from?The simplicity of the central angle formula originates from the definition of a radian. A radian is a unit of angular size, where 1 radian is defined as a central angle (θ) whose arc length is equal to the radius
( The circle angle calculator in terms of pizzaBecause maths can make people hungry, we might better understand the central angle in terms of pizza. What would the central angle be for a slice of pizza if the crust length (L) was equal to the radius (r)? Since the problem defines
How many pizza slices with a central angle of 1 radian could you cut from a circular pizza?In a complete circular pizza, we know that the central angles of all the slices will add up to 2π
radians = 360°. Since each slice has a central angle of 1 radian, we will need We arrive at the same answer if we think this problem in terms of the pizza crust: we know that the circumference of a circle is Now, if you are still hungry, take a look at the sector area calculator to calculate the area of each pizza slice! Bonus challenge - How far does the Earth travel in each season?Try using the central angle calculator in reverse to help solve this problem. The Earth is approximately 149.6 million km away from the Sun. If the Earth travels about one quarter of its orbit each season, how many km does the Earth travel each season (e.g., from spring to summer)? Let's approach this problem step-by-step:
You can try the final calculation yourself by rearranging the formula as:
Then convert the central angle into radians:
When we assume that for a perfectly circular orbit, the Earth travels approximately 234.9 million km each season! FAQHow to find the central angle of a circle?To find the central angle of a circle, use the formula: To find the central angle of a circle, you need to calculate the
ratio of arc length to the radius of a circle. How to find radius with arc length and central angle?To find a radius with arc length and central angle, you need to take calculate the ratio of the arc length and central angle. Angle between two vectorsClock angleComplementary angles… 3 more How do you calculate the central angle?A central angle is defined as the angle subtended by an arc at the center of a circle. The radius vectors form the arms of the angle. A central angle is calculated using the formula: Central Angle = Arc length(AB) / Radius(OA) = (s × 360°) / 2πr, where 's' is arc length, and 'r' is radius of the circle.
How do you find the angle at the center of a circle?(arc length) ÷ circumference = (central angle) ÷ 360°
The central angle will be in degrees. This formula makes sense, if you think about it. The length of the arc out of the total length around the circle (circumference) is the same proportion as the arc's angle out of the total angle in a circle (360 degrees).
How do you find the central angle of a circle without arc length?To calculate arc length without the angle, you need the radius and the sector area: Multiply the area by 2. Then divide the result by the radius squared (make sure that the units are the same) to get the central angle in radians.
What is the central angle of a circle in degrees?The central angle is a quarter of a circle: 360° / 4 = 90° .
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