# area of a sector formula calculator

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

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