If you are still having some trouble understanding this, you can visit Wikipedia’s article on a circular sector. The formula for the area of a sector is (angle / 360) x π x radius2. Just use π = 3.14 and replace the value of r and n into the formula to get the area However, what is a sector? Preview. Calculates the area and arc of an elliptical sector given two axes and two angles. This formula helps you find the area, A, of the sector if you know the central angle in degrees, n °, and the radius, r, of the circle: A = ( n ° 360 ° ) × π × r 2 For your pumpkin pie, plug in 31 ° and 9 inches: To use this online calculator for Perimeter Of Sector, enter Radius (r) and Arc Length (s) and hit the calculate button. Change the values of the angle of the sector and radius of the sector. In this video I go over a pretty extensive and in-depth video in proving that the area of a sector of a circle is equal to 1/2 r^2*θ. Area of a Trapezium formula = 1/2 * (a + b) * h, where a and b are the length of the parallel sides and h is the distance between them. Calculating the Area with a Known Central Angle and Radius 1 Set up the formula A = (θ 360) π r 2 {\displaystyle A=\left ({\frac {\theta } {360}}\right)\pi r^ {2}}. Area of a Sector: Non Calculator (no rating) 0 customer reviews. Area expresses the extent of a two-dimensional shape, in the plane. Calculate the unknown defining side lengths, circumferences, volumes or radii of a various geometric shapes with any 2 known variables. So, if the angle formed is 90 degrees then you would use the formula to find the area of a circle (Pi*r^2) and find the proportion of the entire circle which would be 360 degrees. ... Area calculator with compass eval(ez_write_tag([[300,250],'calculator_academy-banner-1','ezslot_10',192,'0','0']));eval(ez_write_tag([[300,250],'calculator_academy-banner-1','ezslot_11',192,'0','1']));eval(ez_write_tag([[300,250],'calculator_academy-banner-1','ezslot_12',192,'0','2'])); Since a sector is also known as some percentage of a circle, then the area itself is also a portion of the area of a circle. Area of a trapezoid. You can find it by using proportions, all you need to remember is circle area formula (and we bet you do! Download: Use this area calculator offline with our all-in-one calculator app for Android and iOS. The figure below illustrates the measurement: As you can easily see, it is quite similar to that of a circle, but modified to account for the fact that a sector is just a part of a circle. In simple terms it looks like a slice of pie. Area of a sector formula. Area of a Sector Area of a Rectangle Area of a Square Area of a Triangle Area of a Parallelogram Area of a circle formula The formula for the area of a circle is π x radius 2 , but the diameter of the circle is d = 2 x r 2 , so another way to write it is π x (diameter / 2) 2 . eval(ez_write_tag([[300,250],'calculator_academy-large-leaderboard-2','ezslot_18',107,'0','0']));eval(ez_write_tag([[300,250],'calculator_academy-large-leaderboard-2','ezslot_19',107,'0','1']));eval(ez_write_tag([[300,250],'calculator_academy-large-leaderboard-2','ezslot_20',107,'0','2'])); To calculate the area of the sector you must first calculate the area of the equivalent circle using the formula stated previously. The Radius of a Sector Formula calculates the radius by dividing the length of an arc by the value of circumference of π. r is the length of the radius. See how to find the area of the sector (blue area). An arc is a part of the circumference of the circle. For a circle, that entire area is represented by a rotation of 360 degrees. Given, The formula for finding the area of a circle is pi*r*r where r is the radius. Area of a rectangle. Semicircle area formula Knowing the semicircle definition - half of a circle - we can easily write the semicircle area formula using the well-known circle area, πr² : Area semicircle = Area circle / 2 = πr² / 2 The area of a semicircle is just a half of the area of a full circle. Although we do recommend you try to memorize the formula and understand it if you are a student using this as an education resource. Here is how the Perimeter Of Sector calculation can be explained with given input values -> 2.76 = 2.4+2*0.18 . Male Female Age Under 20 years old 20 years old level ... Area of a triangle (Heron's formula) Area of a triangle given base and angles. ): The area of a circle is calculated as A = πr². Now, we will learn about the area of sector, where we measure the central angle (θ) in degrees. Area of a square. Surface area expresses the extent of a two-dimensional surface of a three-dimensional object. :) Read more. The formula for sector area is simple - multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2; But where does it come from? A sector of a circle is the shape formed by slicing up a circular cake. Area of a Sector Formula : $$\text{A}\;=\;\frac{1}{2}θr^2$$ Where, A shows Area of a Sector. The formula is a little complicated to do in your head. The area enclosed by a sector is proportional to the arc length of the sector. For a sector the area is represented by some other angle. Formula : Where, A-Surface Area G-Center of Gravity V-Volume O-Center of the sphere h-Height r-Radius C-Circumference Example: If height is 4 meter and radius is 6 meter , then find the Volume and Area. To understand how to calculate the area of such a sector, it’s important to understand the formula that it uses, which is given above. There is no need to try to remember this confusing formula. The portion of the circle shaded in blue is the sector Select the input value you want, then enter their values. Step 2: Use the proportional relationship. If the two lines are formed at a 180 degree angle then the sector is often referred to as a semi-circle. Whether you want to calculate the Area (A), Arc (s), or one of the other properties of a sector including Radius (r) and the Angle formed, then provide two values of input. When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr² When the angle at the center is 1°, area of the sector = \(\frac{\pi .r ^{2}}{360^{0}}\) Then, you must multiply that area by the ratio of the angles which would be theta/360 since the circle is 360, and theta is the angle of the sector. A sector is part of a circle bounded by two radii and their intercepted arc. A sector is formed by two lines that extend from the midpoint of a circle to any point on the perimeter. Using this formula, and approximating , the area of the circle is . Author: Created by emmat26. Formula to calculate area of a sector of a circle is given below: where, A = Area of a sector of a circle C = Central angle of a circle r = Radius of the circle In the below area of a sector of a circle calculator, enter the central angle and radius in the respective input boxes and click calculate button to find the answer. θ is the angle of the sector. But, if we measure the angle of a circle in radians, the area of sector formula will be AreaofSectorAreaof… What Is The Area of Sector Formula? x is the angle of the sector. Workout : step 1 Address the formula, input parameter and values Radius = 5 in Angle = 45 ° step 2 Find Area of Circle Sector using Radius and Angle values Area A = πr²θ/360 = π x (5)² x 45/360 in² = 22 x 25 x 45/(7 x 360) in² National 5/GCSE Non Calculator, using pi = 3.14. Area of a sector of a circle; Area of a circular segment; Area of an annulus; Area of a sector of an annulus; Area of an ellipse; All formulas for area of plane figures; Surface Area. $$\text{A}\;=\;\frac{x}{360}πr^2$$ Where, A shows Area of a Sector. side a: side b: distance h: Result window. It is enclosed by the two radii from the center of the sphere. For more on this seeVolume of a horizontal cylindrical segment. π = 3.141592654. r = radius of the circle. For example in the figure below, the arc length AB is a quarter of the total circumference, and the area of the sector is a quarter of the circle area. To better understand how to calculate the area of a sector it is important to understand that the angle formed by the two straights sides of the sector is proportional to the are of the circle. Free. Since a sector is also known as some percentage of a circle, then the area itself is also a portion of the area of a circle. It’s a percent or portion of a disk that is enclosed by that arc and two equal radii. Students may use this circle sector calculator to generate work with steps for any other similar input values. This calculation is useful as part of the calculation of the volume of liquid in a partially-filled cylindrical tank. A spherical sector is a solid portion of the sphere cut off by the plane. The formula, solved example & step by step calculations may useful for users to understand how the input values are being used in such sector area calculations. Male or Female ? The formula used to calculate the area of a sector of a circle is: \[Area\,of\,a\,sector = \frac{{Angle}}{{360^\circ }} \times \pi {r^2}\] Example Question. So the area of the sector in this case would be 90/360 or 1/4 of the area of the circle. r is the length of the radius.> In the formula, r = the length of the radius, and θ = the degrees in the central angle of the sector. For a circle, that entire area is represented by a rotation of 360 degrees. Examples of sectors are illustrated below. As, the area of a circle=r2and the angle of a full circle = 360° Thus, the formula of the area of a sector will be: AreaofSectorAreaofCircle=CentralAngle360° AreaofSectorπr2=0360° Area of Sector=0360°∗πr2 r = radius of the circle This formula supports us to find anyone of the values if the other two values are given. All it needs is; the radius and angle to find the area of sector. An easy to use online calculator to calculate the arc length s , the length d of the Chord and the area A of a sector given its radius and its central angle t. Formulas for arc Length, chord and area of a sector Figure 1. formulas for arc Length, chord and area of a sector In the above formulas t is in radians. eval(ez_write_tag([[250,250],'calculator_academy-medrectangle-3','ezslot_1',169,'0','0'])); The area of a sector or arc can be calculated with the following formula: The area of a sector along an arc is also known as the circular sector. Calculator online for a the surface area of a capsule, cone, conical frustum, cube, cylinder, hemisphere, square pyramid, rectangular prism, triangular prism, sphere, or spherical cap. To improve this 'Area of a circular sector Calculator', please fill in questionnaire. Free online calculators for personal use. Just a few questions to practice - there aren't too many about! To use the sector area calculator simply enter the required information into the form fields and our calculator will take care of the complicated calculations for you. Given a radius and an angle, the area of a sector can be calculated by multiplying the area of the entire circle by a ratio of the known angle to 360° or 2π radians, as shown in the following equation: Recall that the angle of a full circle is 360˚ and that the formula for the area of a circle is πr 2. Area of a sector. Online calculators and formulas for a surface area and other geometry problems. 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Degree angle then the sector is formed by two radii from the midpoint of a that..., ellipse, parallelogram, rectangle, rhombus, sector, square,,. = radius of an arc is the radius of the sector ( blue area ) as an education.. X radius2 with our all-in-one calculator app for Android and iOS = 3.14 is! A circle arc and two equal radii unknown defining side lengths, circumferences, volumes or radii of a cake! Values - > 2.76 = 2.4+2 * 0.18 the calculation formula for finding the area of a circle is circumference... Is useful as part of a circle bounded by two lines that extend from the of! This 'Area of a disk that is enclosed by the value of circumference of π input value you,! This formula, r = radius of the sector calculation is useful as part of the sector and radius a! This formula, r = radius of a circle is s a or! 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