Kalkulator lingkaran: luas, keliling dan jari-jari

Temukan luas, keliling, jari-jari dan diameter dari satu nilai. Hitung busur, tali busur, luas juring dan tembereng dari sudut pusat.

Diperbarui 28 September 2026Contoh terverifikasi: 6

Luas

cm²

Tempat desimal maksimum: 4; Terdekat, jika berjarak sama menjauhi nol

Jari-jari: 5cm
Diameter: 10cm
Keliling lingkaran: 31.4159cm
Panjang busur: 5.236cm
Panjang tali busur: 5cm
Luas juring: 13.09cm²
Luas tembereng: 2.2647cm²

A circle of radius 5 cm has diameter 10 cm, circumference 31.4159 cm and area 78.5398 cm². A 60° arc of it is 5.236 cm long, and the chord joining its ends is 5 cm.

Circle, sector and chord

Cara menghitung S

Jari-jari
$r = 5\,\text{cm}$
Diameter and circumference
$d = 2r = 10\,\text{cm},\qquad C = 2\pi r = 2\pi \times 5 = 31.415927\,\text{cm}$
Luas
$A = \pi r^2 = \pi \times 5^2 = 78.539816\,\text{cm}^{2}$
Arc length and chord
$s = r\theta = 5 \times \frac{60\pi}{180} = 5.235988\,\text{cm},\qquad c = 2r\sin\frac{\theta}{2} = 2 \times 5 \times \sin 30^\circ = 5\,\text{cm}$
Sector and segment areas
$A_\text{sector} = \pi r^2 \frac{\theta}{360^\circ} = 13.089969\,\text{cm}^{2},\qquad A_\text{segment} = \frac{r^2}{2}\left(\theta - \sin\theta\right) = 2.264652\,\text{cm}^{2}$
The segment is the region between the chord and the arc; θ is in radians inside the bracket.

Tentang Kalkulator lingkaran: luas, keliling dan jari-jari

Give any one of the radius, diameter, circumference or area and the other three follow from d = 2r, C = 2πr and A = πr². For a central angle θ the calculator also returns the arc length s = rθ (θ in radians), the chord c = 2r sin(θ/2), the sector area πr² × θ/360° and the segment area r²/2 × (θ − sin θ).

The default radius of 5 cm gives a diameter of 10 cm, a circumference of 31.4159 cm and an area of 78.5398 cm². Its 60° arc is 5.236 cm long and the chord across it is exactly 5 cm, because two radii and that chord form an equilateral triangle. Starting from the circumference suits trees, pipes and columns whose diameter cannot be reached: a girth of 100 cm means a diameter of 31.831 cm.

Inputs can be in any length or area unit, including hectares and acres, and every result appears in the unit chosen under "Show results in". The central angle must be above 0° and at most 360°; at 360° the segment is the whole disc.

Contoh penyelesaian

Jari-jari 5 cm, busur 60°

Ukuran yang diketahui: Jari-jari
Jari-jari: 5 cm
Sudut pusat untuk busur dan tali busur: 60 °
Satuan hasil: Sentimeter (cm)

Luas: 78.539816 cm²
Keliling lingkaran: 31.415927 cm
Diameter: 10 cm
Panjang busur: 5.235988 cm
Panjang tali busur: 5 cm
Luas juring: 13.089969 cm²

Sumber pemeriksaan: Python 3.8 math: pi*5**2, 2*pi*5, 5*radians(60), 2*5*sin(radians(30)) = 5 (equilateral triangle), pi*25*60/360

Keliling 100 cm

Ukuran yang diketahui: Keliling lingkaran
Keliling lingkaran: 100 cm
Sudut pusat untuk busur dan tali busur: 60 °
Satuan hasil: Sentimeter (cm)

Jari-jari: 15.915494 cm
Luas: 795.774715 cm²
Diameter: 31.830989 cm

Sumber pemeriksaan: Python 3.8 math: 100/(2*pi), 100**2/(4*pi)

Luas 1 m², hasil dalam meter

Ukuran yang diketahui: Luas
Luas: 1 m²
Sudut pusat untuk busur dan tali busur: 60 °
Satuan hasil: Meter (m)

Jari-jari: 0.56419 m
Keliling lingkaran: 3.544908 m

Sumber pemeriksaan: Python 3.8 math: sqrt(1/pi), 2*sqrt(pi)

Diameter 12 in, busur seperempat lingkaran

Ukuran yang diketahui: Diameter
Diameter: 12 in
Sudut pusat untuk busur dan tali busur: 90 °
Satuan hasil: Inci (in)

Panjang tali busur: 8.485281 in
Luas juring: 28.274334 in²
Luas tembereng: 10.274334 in²
Panjang busur: 9.424778 in

Sumber pemeriksaan: Python 3.8 math: 12*sin(pi/4), 36*pi/4, 36*pi/4 − 18, 6*pi/2

Pertanyaan

How do you find the area of a circle from the diameter?

Use A = πd²/4, which is πr² with the radius written as half the diameter. A 10 cm diameter gives 25π ≈ 78.54 cm², and a 12 in pizza covers 36π ≈ 113.10 in². Area grows with the square of the diameter, so one 16 in pizza (201.06 in²) has more area than two 11 in pizzas together (190.07 in²).

How do you find the radius from the circumference?

Divide the circumference by 2π: r = C/(2π). A tree with a girth of 100 cm has a radius of 15.915 cm and a diameter of 31.831 cm (C/π). Foresters' diameter tapes do this division for you: their scale is graduated in units of π, so wrapping the tape round the trunk reads the diameter directly.

What is the difference between a sector and a segment of a circle?

A sector is the pie slice between two radii and the arc; a segment is the region between the arc and the chord joining its ends. The segment is the sector minus the triangle formed by the two radii and the chord. For a 90° slice of a circle with a 6 in radius, the sector is 9π ≈ 28.274 in², the triangle 18 in², and the segment 10.274 in².

How do you calculate arc length?

Multiply the radius by the central angle in radians: s = rθ. With the angle in degrees, use s = 2πr × θ/360. A 60° arc on a 5 cm radius is 5 × π/3 ≈ 5.236 cm, one sixth of the 31.416 cm circumference. Putting degrees straight into s = rθ gives an answer 57.3 times too large, the number of degrees in one radian.

Is 3.14 accurate enough for pi?

For estimates, yes. 3.14 is 0.05% below π, so a 5 cm radius gives an area of 78.5 cm² instead of 78.54 cm²; the fraction 22/7 is 0.04% too high. The absolute error grows with size: for a radius of 100 m, 3.14 gives 31,400 m², which is 15.9 m² short of the true 31,415.9 m².

Seberapa akurat “Kalkulator lingkaran: luas, keliling dan jari-jari”?

Akurasi bergantung pada masukan dan asumsi metode. Aritmetika desimal memakai 50 digit signifikan, tetapi perkiraan, metode numerik dan data sumber bisa kurang presisi; pembulatan yang ditampilkan tidak menghilangkan batasan itu. Contoh penyelesaian yang diperiksa dengan sumber independen: 6. Misalnya, “Jari-jari 5 cm, busur 60°” diperiksa dengan Python 3.8 math: pi*5**2, 2*pi*5, 5*radians(60), 2*5*sin(radians(30)) = 5 (equilateral triangle), pi*25*60/360.

Dari mana metode ini berasal?

Weisstein, E. W. “Circle”, “Circular Segment” — MathWorld; NIST Digital Library of Mathematical Functions §3.12 — mathematical constant π.

Tentang kalkulator ini

\begin{gathered} A = \pi r^2,\quad C = 2\pi r,\quad s = r\theta \\ c = 2r\sin\tfrac{\theta}{2},\quad A_\text{segment} = \tfrac{r^2}{2}(\theta - \sin\theta) \end{gathered}

Sumber

Diperiksa dengan referensi

Kalkulator ini mencakup 6 contoh perhitungan dengan jawaban dari sumber independen. Contoh tersebut dijalankan dalam rangkaian pengujian dan dapat Anda jalankan di sini juga.