⭕ Circle Calculator (in Terms of π)
r = 6 → area = 36π, circumference = 12π — the "in terms of π" form the homework asks for, plus arc length and sector area for any central angle, exact.
36π
≈ 113.09734
area (πr²)
12π
≈ 37.699112
circumference (2πr)
6
radius
12
diameter
2π
≈ 6.2831853
arc length for 60° (θ/360 · 2πr)
6π
≈ 18.849556
sector area for 60° (θ/360 · πr²)
Working
- Area = πr² = π · (6)² = 36π
- Circumference = 2πr = 2π · 6 = 12π
- Arc = (θ/360) · 2πr = (60/360) · 12π = 2π
Answers "in terms of π" — r = 6 gives area 36π, exactly what the homework asks for — with decimals alongside. Runs locally.
How the circle calculator (in terms of π) works
Every result is computed as an exact rational coefficient of π and displayed that way: area πr², circumference 2πr, and — given a central angle θ — arc length (θ/360)·2πr and sector area (θ/360)·πr², each with the substitution working shown and a decimal approximation alongside. The radius (or diameter — the tool converts) accepts integers, decimals and fractions, so r = 3/2 gives area 9π/4 exactly. Nothing is rounded until the optional decimal at the very end.
"Give your answer in terms of π" is one of the most common instructions in geometry — and almost every online circle calculator ignores it, jumping straight to 113.097. The symbolic form isn't pedantry: it's exact (π is irrational; any decimal is wrong somewhere), it cancels cleanly in later algebra, and it's the marked answer. The decimal is there too, for when you actually need to cut the material.
Frequently asked questions
What does "in terms of π" mean?
Leave π as a symbol instead of substituting 3.14159…: a circle of radius 6 has area 36π exactly, of which 113.097 is only an approximation. Geometry courses usually require the symbolic form.
What are the circle formulas?
Area = πr², circumference = 2πr (or πd), arc length = (θ/360)·2πr and sector area = (θ/360)·πr² for a central angle θ in degrees. The tool applies each with your values and shows the substitution.
Can I enter the diameter instead of the radius?
Yes — switch the selector; the tool halves it exactly (d = 7 gives r = 7/2 and area 49π/4).
How are arc length and sector area related?
Both scale the full circle by the same angle fraction θ/360 — arc scales the circumference, sector scales the area. A 60° slice is exactly one sixth of each.
Is anything rounded?
The π-coefficients are exact rationals throughout; only the optional decimal display approximates. Runs locally.