Question 1

How do I convert degrees to radians?

Accepted Answer

To convert degrees to radians, multiply by π/180 (approximately 0.0174533). For example, 180° = 180 × π/180 = π radians ≈ 3.14159 rad. Our converter performs this calculation automatically with high precision when you enter a degree value. Radians are essential in calculus and advanced mathematics.

Question 2

How do I convert radians to degrees?

Accepted Answer

To convert radians to degrees, multiply by 180/π (approximately 57.2958). For example, π radians = π × 180/π = 180°. Simply enter your radian value and get instant conversion to degrees and other units. This is commonly needed in mathematics, physics, and engineering.

Question 3

What are gradians and why are they used?

Accepted Answer

Gradians (also called gons or grades) are a unit where a right angle is 100 gradians and a full circle is 400 gradians. They are sometimes used in surveying and civil engineering, particularly in Europe. 90° = 100 gradians = π/2 radians. Gradians make some calculations simpler because 100 is a decimal-friendly number.

Question 4

What is a turn in angle measurement?

Accepted Answer

A turn (also called a revolution or rotation) represents one complete circle or 360°. 1 turn = 360° = 2π radians = 400 gradians. It's useful for describing rotational motion, circular movements, and angles greater than 360°. For example, 1.5 turns means one and a half complete rotations.

Question 5

Which angle unit should I use?

Accepted Answer

Degrees (°) are most common for everyday use, geometry, and navigation. Radians (rad) are preferred in mathematics, physics, and calculus because they simplify many formulas. Gradians are mainly used in surveying. Turns are useful for rotational descriptions. Choose based on your field: degrees for general use, radians for advanced math.

Question 6

Why are radians important in mathematics?

Accepted Answer

Radians are the natural unit for angles in mathematics because they relate angles directly to arc length. In a circle with radius r, an angle of θ radians creates an arc of length r×θ. This makes calculus formulas simpler: d/dx(sin x) = cos x only works when x is in radians. Radians are dimensionless and fundamental to trigonometry.

Question 7

How many radians are in a circle?

Accepted Answer

A complete circle contains 2π radians (approximately 6.28319 radians). This comes from the fact that the circumference of a circle is 2πr, so when r=1, the arc length around the entire circle is 2π. Half a circle (180°) is π radians, a quarter circle (90°) is π/2 radians.

Question 8

What are common angle conversions?

Accepted Answer

Common conversions: 30° = π/6 rad ≈ 0.524 rad, 45° = π/4 rad ≈ 0.785 rad, 60° = π/3 rad ≈ 1.047 rad, 90° = π/2 rad ≈ 1.571 rad, 180° = π rad ≈ 3.142 rad, 360° = 2π rad ≈ 6.283 rad. Our converter provides instant results for any angle value.

Angle	Degrees	Radians	Gradians
Zero	0°	0 rad	0 grad
Acute	45°	π/4 ≈ 0.785 rad	50 grad
Right	90°	π/2 ≈ 1.571 rad	100 grad
Obtuse	135°	3π/4 ≈ 2.356 rad	150 grad
Straight	180°	π ≈ 3.142 rad	200 grad
Full Circle	360°	2π ≈ 6.283 rad	400 grad

Angle Converter

Angle Converter

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