Tangent Angle Calculator — tan(θ)
Enter an angle in degrees or radians to instantly get tan(θ), along with sin, cos, cot, and sec — plus a live graph showing where your angle lands on the tangent curve.
°
Angle unit
Tangent = opposite ÷ adjacent = sin(θ) ÷ cos(θ)
- 1
Angle in radians
45 × π ÷ 180 = 0.785398 - 2
sin(θ)
0.707107 - 3
cos(θ)
0.707107 - 4
tan(θ) = sin(θ) ÷ cos(θ)
0.707107 ÷ 0.707107 = 1
How does this calculator work?
tan(θ) = sin(θ)/cos(θ) = opposite/adjacent. Enter any angle in degrees or radians — the result also shows sin, cos, cot, and sec. Tangent is undefined at ±90°, ±270° etc. (asymptotes) and repeats every 180°. Key values: tan(0°) = 0, tan(45°) = 1, tan(60°) = √3 ≈ 1.732.
Formula
How this is calculated
The tangent of an angle θ is the ratio of the sine to the cosine: tan(θ) = sin(θ)/cos(θ). In a right triangle it equals the ratio of the side opposite θ to the side adjacent to θ. On the unit circle it is the length of the segment from the point (1, 0) up to the line through the origin and the circle point, a construction that makes the asymptotic behaviour at 90° immediately visible.
The tangent function is defined for all angles except 90° + n×180° (n any integer), where cos(θ) = 0 and the ratio blows up to ±∞. The function has period 180° (π rad), not 360° like sine and cosine, because tan(θ + 180°) = tan(θ) — shifting by half a revolution returns the same value. The graph plot is shown over the range (−80°, 80°) to avoid the asymptotes; values beyond ±15 are clipped for readability.
The secant sec(θ) = 1/cos(θ) and cotangent cot(θ) = cos(θ)/sin(θ) are derived from the same angle. Cot is undefined where sin(θ) = 0, i.e. at 0° and 180°. IEEE 754 floating point is used throughout; near-asymptote angles may show very large but finite numbers due to rounding.
Frequently asked questions
tan(45°) = 1 exactly, because in a 45-45-90 triangle the two legs are equal, so opposite/adjacent = 1. Equivalently, sin(45°) = cos(45°) = 1/√2, so their ratio is 1.
At 90°, cos(90°) = 0, and tan = sin/cos would require dividing by zero. Geometrically, the adjacent side has zero length, so opposite/adjacent has no finite value. The tangent function approaches +∞ from the left and −∞ from the right of 90°.
The tangent function repeats every 180° (π radians) — half the period of sine and cosine. This is because tan(θ + 180°) = sin(θ + 180°)/cos(θ + 180°) = −sin(θ)/−cos(θ) = tan(θ).
Also known as
TG we-Calculate Editorial Team. (2026). Tangent Angle Calculator — tan(θ) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/tangent-angle-calculator
TG we-Calculate Editorial Team. "Tangent Angle Calculator — tan(θ)." TG we-Calculate. 2026. https://we-calculate.com/calculator/tangent-angle-calculator.
TG we-Calculate Editorial Team, "Tangent Angle Calculator — tan(θ)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/tangent-angle-calculator
@misc{wecalculate_tangent_angle_calculator, title = {Tangent Angle Calculator — tan(θ)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/tangent-angle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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