Kalkulator długości łuku i pola wycinka koła
Ten kalkulator znajduje długość łuku, pole wycinka i długość cięciwy na podstawie promienia i kąta środkowego. Kąty mogą być w stopniach lub radianach; w stopniach odpowiedzi podawane są dokładnie w postaci z π oraz jako ułamki dziesiętne.
Wynik
Wpisz wartości i naciśnij Oblicz, aby zobaczyć wynik.
Wzór
The arc is the same fraction of the circumference as the angle is of a full turn.
The sector is the same fraction of the whole circle’s area.
The chord is the straight line joining the ends of the arc.
Jak korzystać z tego kalkulatora
- Enter the radius and the central angle, and choose degrees or radians.
- Press Calculate to see the arc length, sector area and chord length.
Rozwiązane przykłady
Radius 6, angle 60°
60° is 1/6 of a full turn. Arc = 1/6 × 2π × 6 = 2π ≈ 6.283185.
Sector area = 1/6 × π × 36 = 6π ≈ 18.849556.
Chord = 2 × 6 × sin 30° = 6.
Radius 4, angle 1.5 radians
Arc = rθ = 4 × 1.5 = 6.
Area = ½ × 16 × 1.5 = 12.
Chord = 2 × 4 × sin 0.75 ≈ 5.45311.
A semicircle: radius 10, angle 180°
Arc = half the circumference = 10π.
Area = half the circle = 50π. The chord is the diameter, 20.
Częste błędy
- Using s = rθ with θ in degrees; that formula needs radians.
- Mixing up the diameter and the radius.
- Confusing the arc (curved) with the chord (straight).
Najczęstsze pytania
How do you find the arc length?
Arc length = (θ/360°) × 2πr for θ in degrees, or s = rθ for θ in radians. For r = 6 and 60°: (60/360) × 12π = 2π.
How do you find the area of a sector?
Area = (θ/360°) × πr², or ½r²θ in radians. A 90° sector of radius 4 has area ¼ × 16π = 4π.
What is the difference between an arc and a chord?
The arc is the curved part of the circle between two points; the chord is the straight line joining them.