Circle Calculator
Units
Significant Figures
Answer:
circumference
C = 75.3982237 in
In Terms of Pi π
circumference
C = 24 π in
Solutions
\[ \textbf{diameter} \, d = 2r \]\[d = 2 \times 12 \]\[d = 24 \]
\[ \textbf{circumference} \, C = 2 \pi r \]\[C = 2 \times \pi \times 12 \]\[C = 24 \pi \]\[C = 75.3982237 \]
\[ \textbf{area} \, A = \pi r^2 \]\[A = \pi \times 12^2 \]\[A = 144 \pi \]\[A = 452.389342 \]
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Circle Shape
r = radius
d = diameter
C = circumference
A = area
π = pi = 3.1415926535898
√ = square root
Calculator Use
Use this circle calculator to find the area, circumference, radius or diameter of a circle. Given any one variable A, C, r or d of a circle you can calculate the other three unknowns.
Units: Note that units of length are shown for convenience. They do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft2 or ft3. Any other base unit can be substituted.
Circle Formulas in terms of Pi π, radius r, and diameter d
Radius and Diameter:
r = d/2
d = 2rArea of a circle:
A = πr2 = πd2/4
Circumference of a circle:
C = 2πr = πd
Circle Calculations:
Using the formulas above and additional formulas you can calculate properties of a given circle for any given variable.
Calculate A, C and d | Given r
Given the radius of a circle calculate the area, circumference and diameter. Putting A, C and d in terms of r the equations are:
\[A = \pi r^2 \]
\[C = 2 \pi r \]
\[d = 2r \]
Calculate r, C and d | Given A
Given the area of a circle calculate the
radius, circumference and diameter. Putting r, C and d in terms of A the equations are:
\[r = \sqrt{\frac{A}{\pi}} \]
\[C = 2 \pi r = 2 \pi \sqrt{\frac{A}{\pi}} \]
\[ d = 2r = 2 \sqrt{\frac{A}{\pi}} \]
Calculate A, r and d | Given C
Given the circumference of a circle calculate the radius, area and diameter. Putting A, r and d in terms of C the equations are:
\[r = \frac{C}{2 \pi} \]
\[A = \pi r^2 = \pi \left(\frac{C}{2 \pi}\right)^2 = \frac{\pi C^2}{4 \pi^2} = \frac{C^2}{4 \pi} \]
\[d = 2r = \frac{2C}{2 \pi} = \frac{C}{\pi} \]
Calculate A, C and r | Given d
Given the diameter of a circle calculate the radius, area and circumference. Putting A, C and r in terms of d the equations are:
\[r = \frac{d}{2} \]
\[A = \pi r^2 = \pi \left(\frac{d}{2}\right)^2 = \frac{\pi d^2}{4} \]
\[C = 2 \pi r = 2 \pi \frac{d}{2} = \pi d \]
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Solved Example
The below solved example problem may be useful to understand how the values are being used in the mathematical formulas to find the sector area of a circle.
Example Problem :Find the area of circular sector having the radius r = 18 cm and sector angle 25.?
Solution :The given values
radius r = 18 cm
sector angle θ = 25.
formula
to find sector area = (π r2 θ) / 360
substitute the values
= (π x 182 x 25)/360
= 70.71 cm2
The sector area of a circle may required to be calculated in SI or metric or US customary unit systems, therefore this sector calculator is featured with major measurement units conversion function to find the output values in different customary units such as inches (in), feet (ft), meters (m), centimeters (cm) & millimeters (mm) by using this below conversion table.
| 10 mm = 1 cm 100 mm = 3.93 in 1000 mm = 3.28 ft 1000 mm = 1 m | 1 cm = 10 mm 10 cm = 3.93 in 100 cm = 3.28 ft 100 cm = 1 m | 1 ft = 3048 mm 1 ft = 304.8 cm 1 ft = 12 in 10 ft = 3.048 m | 1 in = 25.4 mm 1 in = 2.54 cm 100 in = 8.33 ft 100 in = 2.54 m |
In the field of area & volume calculations, finding the sector area of a circle is important to understand basic mathematical computations. The above formulas, step by step calculation & solved example may helpful for users to understand the how to calculate circle's sector area manually, however, when it comes to online to perform quick calculations, this circle's sector area calculator may be useful to find the results.