# area of a sector formula calculator

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

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