Tangent Ratio Calculator — tan(θ) in Right Triangles
Use this calculator to work out the tangent ratio (tan θ = opposite ÷ adjacent) for any right triangle. Give an angle and a side, or give two sides, and get the missing values — plus sin, cos, and hypotenuse — instantly.
Solve for
°
tan(35°) × 10 = 7
- 1
Angle to radians
35 × π ÷ 180 = 0.6109 - 2
tan(θ)
0.7002 - 3
Opposite = adjacent × tan(θ)
10 × 0.7002 = 7
How does this calculator work?
tan(θ) = opposite ÷ adjacent. Enter the angle and adjacent side to find the opposite side and hypotenuse, or enter both legs to find the angle. The calculator also returns sin(θ), cos(θ), and all three sides, backed by a right-triangle diagram.
Formula
How this is calculated
The tangent ratio is one of three primary trigonometric ratios used with right triangles (the familiar SOH-CAH-TOA). For an angle θ measured from one of the non-right vertices, the tangent is the ratio of the side directly opposite that angle to the side directly adjacent to it: tan(θ) = opposite ÷ adjacent.
If you know the angle and the adjacent side, multiplying by tan(θ) gives the opposite side; dividing by cos(θ) or applying the Pythagorean theorem gives the hypotenuse. If instead you know both legs of the right triangle, dividing opposite by adjacent gives the tangent value, and applying the inverse tangent (arctan) recovers the angle in degrees.
Note that all trig ratios are defined only for angles strictly between 0° and 90° in a right triangle. In the context of unit-circle trigonometry, tan(θ) extends to all angles except odd multiples of 90° where the function is undefined. This calculator covers the right-triangle case only.
Frequently asked questions
The tangent of an angle in a right triangle tells you how many units of opposite side there are for every unit of adjacent side. A tan(θ) of 1 means the opposite and adjacent legs are equal (θ = 45°); greater than 1 means the opposite is longer; less than 1 means the adjacent is longer.
Divide the opposite side by the adjacent side to get the tangent value, then apply the inverse tangent function (arctan, or tan⁻¹ on a calculator) to get the angle in degrees. This calculator does that automatically when you select "Find angle (given opposite + adjacent)".
At θ = 90° the adjacent side shrinks to zero, so tan(90°) = opposite ÷ 0, which is undefined (or infinite). In practice, angles in a right triangle must stay strictly between 0° and 90° for the ratios to make sense.
Also known as
TG we-Calculate Editorial Team. (2026). Tangent Ratio Calculator — tan(θ) in Right Triangles [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/tangent-ratio-calculator
TG we-Calculate Editorial Team. "Tangent Ratio Calculator — tan(θ) in Right Triangles." TG we-Calculate. 2026. https://we-calculate.com/calculator/tangent-ratio-calculator.
TG we-Calculate Editorial Team, "Tangent Ratio Calculator — tan(θ) in Right Triangles," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/tangent-ratio-calculator
@misc{wecalculate_tangent_ratio_calculator, title = {Tangent Ratio Calculator — tan(θ) in Right Triangles}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/tangent-ratio-calculator}}, year = {2026}, note = {TG we-Calculate} }
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