Formules

Calculatrice de longueur d’arc et d’aire de secteur

Cette calculatrice trouve la longueur d’un arc, l’aire du secteur et la longueur de la corde à partir du rayon et de l’angle au centre. Les angles peuvent être en degrés ou en radians ; en degrés, les réponses sont données exactement en fonction de π ainsi qu’en décimal.

Résultat

Saisissez les valeurs et appuyez sur Calculer pour voir le résultat.

Formule

s=θ360∘×2πr=rθ (θ in radians)s = \frac{\theta}{360^\circ} \times 2\pi r = r\theta \ (\theta \text{ in radians})

The arc is the same fraction of the circumference as the angle is of a full turn.

A=θ360∘×πr2=12r2θA = \frac{\theta}{360^\circ} \times \pi r^2 = \tfrac{1}{2} r^2 \theta

The sector is the same fraction of the whole circle’s area.

c=2rsin⁡θ2c = 2r\sin\frac{\theta}{2}

The chord is the straight line joining the ends of the arc.

Comment utiliser cette calculatrice

  1. Enter the radius and the central angle, and choose degrees or radians.
  2. Press Calculate to see the arc length, sector area and chord length.

Exemples corrigés

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.

Erreurs fréquentes

  • 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).

Questions fréquentes

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.