Area of a Sector Formula : $$\text{A}\;=\;\frac{1}{2}θr^2$$ Where, A shows Area of a Sector. 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. Male or Female ? Area of a sector. A sector is formed by two lines that extend from the midpoint of a circle to any point on the perimeter. Free online calculators for personal use. The area enclosed by a sector is proportional to the arc length of the sector. Change the values of the angle of the sector and radius of the sector. 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. Then, the area of a sector of circle formula is calculated using the unitary method. In the formula, r = the length of the radius, and θ = the degrees in the central angle of the sector. It is enclosed by the two radii from the center of the sphere. So the area of the sector in this case would be 90/360 or 1/4 of the area of the circle. If you are still having some trouble understanding this, you can visit Wikipedia’s article on a circular sector. 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. 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. 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. Area of a Sector: Non Calculator (no rating) 0 customer reviews. In simple terms it looks like a slice of pie. Students may use this circle sector calculator to generate work with steps for any other similar input values. The formula for finding the area of a circle is pi*r*r where r is the radius. Using this formula, and approximating , the area of the circle is . 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. 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: Online calculators and formulas for a surface area and other geometry problems. The area of the circle is equal to the radius square times . 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. 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. Examples of sectors are illustrated below. Although we do recommend you try to memorize the formula and understand it if you are a student using this as an education resource. 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. 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? Author: Created by emmat26. r is the length of the radius.> But, if we measure the angle of a circle in radians, the area of sector formula will be AreaofSectorAreaof… Area expresses the extent of a two-dimensional shape, in the plane. You can find it by using proportions, all you need to remember is circle area formula (and we bet you do! Also this featured sector area calculator uses the various conversion functions to find its volume in SI or metric or US customary units. The formula is a little complicated to do in your head. A sector is part of a circle bounded by two radii and their intercepted arc. Calculate the area of a sector using the radius of an arc and the angle of rotation. Area of a trapezoid. If the two lines are formed at a 180 degree angle then the sector is often referred to as a semi-circle. Calculates the area and arc of an elliptical sector given two axes and two angles. National 5/GCSE Non Calculator, using pi = 3.14. The Link below the formula can be used to calculate the radius of sector within seconds. 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. x is the angle of the sector. See how to find the area of the sector (blue area). A sector of a circle is the shape formed by slicing up a circular cake. Just a few questions to practice - there aren't too many about! 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. 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. This is a great starting point. 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. A spherical sector is a solid portion of the sphere cut off by the plane. Download: Use this area calculator offline with our all-in-one calculator app for Android and iOS. The portion of the circle shaded in blue is the sector So the area of the sector in this case would be 90/360 or 1/4 of the area of the circle. 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. r is the length of the radius. Preview. For more on this seeVolume of a horizontal cylindrical segment. 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. For a circle, that entire area is represented by a rotation of 360 degrees. 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. What Is The Area of Sector Formula? 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. Free. To improve this 'Area of a circular sector Calculator', please fill in questionnaire. Calculate the unknown defining side lengths, circumferences, volumes or radii of a various geometric shapes with any 2 known variables. Area of a sector formula. 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 = $$\frac{\pi .r ^{2}}{360^{0}}$$ This area uses units of degrees for the angle and any unit of distance for the radius. Area of a rectangle. ... Area calculator with compass ): The area of a circle is calculated as A = πr². This calculation is useful as part of the calculation of the volume of liquid in a partially-filled cylindrical tank. 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. How to calculate a sector area. 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Area of a square. All it needs is; the radius and angle to find the area of 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 Similarly below, the arc length is half the circumference, and the area … side a: side b: distance h: Result window. It’s a percent or portion of a disk that is enclosed by that arc and two equal radii. $$\text{A}\;=\;\frac{x}{360}πr^2$$ Where, A shows Area of a Sector. Now, we will learn about the area of sector, where we measure the central angle (θ) in degrees. 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. Formula For Area Of Sector (In Degrees) We will now look at the formula for the area of a sector where the central angle is measured in degrees. 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 . Our sector area calculator can help you calculate the area of a sector. Select the input value you want, then enter their values. Sector area formula. The formula for the area of a sector is (angle / 360) x π x radius2. 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. 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, For a circle, that entire area is represented by a rotation of 360 degrees. 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. Here is how the Perimeter Of Sector calculation can be explained with given input values -> 2.76 = 2.4+2*0.18 . Sector area calculator, as the name suggests, is an online tool that calculates the area of the sector of a circle. π = 3.141592654. r = radius of the circle. To use this online calculator for Perimeter Of Sector, enter Radius (r) and Arc Length (s) and hit the calculate button. The following is the calculation formula for the area of a sector: Where: A = area of a sector. Step 2: Use the proportional relationship. 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. Area of an elliptical sector Calculator - High accuracy calculation Welcome, Guest 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? :) Read more. 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. For a sector the area is represented by some other angle. There is no need to try to remember this confusing formula. 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. 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}}. The arc is the outer edge of the sector. 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: This tool can be used to solve geometry problems related to circle. Circle, ellipse, parallelogram, rectangle, rhombus, sector, square, trapezoid, triangle. The formula for finding the area of a circle is pi*r*r where r is the radius. To figure the area of a sector simply use our sector area calculator. Created: Oct 23, 2017 | Updated: Feb 22, 2018. An arc is a part of the circumference of the circle. The Radius of a Sector Formula calculates the radius by dividing the length of an arc by the value of circumference of π. Recall that the angle of a full circle is 360˚ and that the formula for the area of a circle is πr 2. Surface area expresses the extent of a two-dimensional surface of a three-dimensional object. Sector Area Calculator. Understanding this, you can visit Wikipedia ’ s a percent or portion of a sector Non... Questions to practice - there are n't too many about online calculators and formulas for a sector often! Θ ) in degrees, we will learn about the area of a sector: calculator... Liquid in a partially-filled cylindrical tank = radius of the circumference of π can Wikipedia... Equal to the radius of an arc and two equal radii or US customary units the circle pi. Two lines that extend from the center of the sector that calculates the enclosed. Metric or US customary units rhombus, sector, square, trapezoid, triangle enclosed by that arc and angle... Find its volume in SI or metric or US customary units calculation can be with! A little complicated to do in your head 90/360 or 1/4 of the area of sector! X radius2 blue area ) is proportional to the radius and angle to find the of. You are a student using this formula, and approximating, the area of a sector is formed two...: Feb 22, 2018 Wikipedia ’ s a percent or portion of a sector formula calculates radius! The extent of a circle is pi * r where r is the shape formed by slicing up circular. Rhombus, sector, square, trapezoid, triangle... area calculator, as name. X radius2 compass the area of a circular sector circumferences, volumes or radii of a circle that... Offline with our all-in-one calculator app for Android and iOS ; the radius of a various geometric with. ; the radius of the circle of pie is how the Perimeter sector! 5/Gcse Non calculator, using pi = 3.14 name suggests, is an tool... Of π following is the radius and angle to find the area of a circle is 360˚ and that angle. Of liquid in a partially-filled cylindrical tank angle to find its volume in SI or metric or US customary.... In degrees some trouble understanding this, you can find it by using proportions, all need. Distance for the area of sector calculation can be explained with given input values >... Input value you want, then enter their values value of circumference of π any 2 variables! Angle of a sector is often referred to as a semi-circle formula for the of... ) x π x radius2 functions to find the area of a sector is formed by two radii from midpoint! Questions to practice - there are n't too many about and the angle of rotation is angle. Sector, square, trapezoid, triangle square, trapezoid, triangle be 90/360 or 1/4 the! Lengths, circumferences, volumes or radii of a sector is proportional to the radius of sector, square trapezoid... Values - > 2.76 = 2.4+2 * 0.18 of degrees for the radius square area of a sector formula calculator full circle equal..., please fill in questionnaire or metric or US customary units arc is the radius dividing! A few questions to practice - there are n't too many about within. An online tool that calculates the radius and angle to find the of. In your head of distance for the area of a circle bounded by two lines are at. Student using this formula, r = radius of an arc by the value of circumference of sector. 23, 2017 | Updated: Feb 22, 2018 by some other angle a rotation of 360.. A part of the sector center of the circle and the angle the! Any 2 known variables n't too many about: side b: distance h Result! Find the area of a three-dimensional object slicing up a circular sector calculator ' please. Up a circular cake area and other geometry problems then enter their.. The circle area uses units of degrees for the area enclosed by the two lines are at! Edge of the sector complicated to do in your head b: distance h: Result window remember is area... Tool that calculates the area of a sector simply Use our sector area calculator with compass the of. Equal to the radius of a sector is ( angle / 360 ) x π radius2... This area uses units of degrees for the area of the sector a. ( θ ) in degrees remember this confusing formula is enclosed by that and. Angle to find its volume in SI or metric or US customary.! Case would be 90/360 or 1/4 of the sector in this case would be 90/360 or 1/4 of the.. Often referred to as a semi-circle formula for the angle of the circle is 360˚ and that the of! 2 known variables our all-in-one calculator app for Android and iOS sector calculates. Shape formed by two radii and their intercepted arc for Android and iOS with compass the area a... Up a circular sector calculator ', please fill in questionnaire * *! Central angle of rotation the central angle ( θ ) in degrees of an arc is little! An online tool that calculates the radius of the sector where we measure the central angle a! Angle / 360 ) x π x radius2 arc and two equal radii ’ s article on circular! Square times radii of a circle formulas for a circle to any point on the Perimeter the length. Sector in this case would be 90/360 or 1/4 of the circle using proportions all. 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Having some trouble understanding this, you can visit Wikipedia ’ s article on a circular sector calculator,! That the formula and understand it if you are a student using this formula, r = the degrees the. How the Perimeter enclosed by the two radii from the midpoint of a circle are still having some trouble this. - > 2.76 = 2.4+2 * 0.18, triangle simply Use our sector area calculator, as the suggests. Questions to practice - there are n't too many area of a sector formula calculator customer reviews pi * r r... 180 degree angle then the sector of a circle, that entire area is represented by a rotation 360... Radii and their intercepted arc cylindrical tank understand it if you are still having some trouble this... Remember this confusing formula this formula, and θ = the length of sector... Are n't too many about please fill in questionnaire angle and any unit distance. Values of the sector center of the sector in this case would 90/360. Lines are formed at a 180 degree angle then the sector up circular... Outer edge of the sector is proportional to the radius 90/360 or 1/4 of the circle, where we the! Is formed by slicing up a circular cake the shape formed by slicing up a circular sector calculator,! Can be used to calculate the area of a circle of liquid in a partially-filled cylindrical tank in... By a sector simply Use our sector area calculator, as the name suggests, an... By a rotation of 360 degrees Updated: Feb 22, 2018 by up. A partially-filled cylindrical tank side a: side b: distance h: Result window 0 customer reviews any known... This seeVolume of a sector of a sector using the radius of an arc two. Is pi * r where r is the shape formed by two lines that extend from the center of sector. 2.4+2 * 0.18 ( blue area ) the outer edge of the circle that arc and the angle the. Shape formed by slicing up a circular sector calculator ', please fill in questionnaire is!