Math

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Tangent Ratio Calculator.

Calculate tan(theta) from opposite and adjacent right-triangle sides.

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01

Set your values

Results update as you type.

opposite: 3

opposite

0.000000
adjacent: 4

adjacent

0.000000
Tangent: 0.75

Tangent

0.000000
Angle (degrees): 36.869898

Angle (degrees)

0.000000

Results update automatically as you type.

Use Cases

Solve trigonometry homework problems

Quickly verify your manual calculations for tangent ratios in right triangles, saving time and reducing errors.

Example: Given opposite = 3 and adjacent = 4, the tangent ratio is 0.75.

Estimate slopes or angles in construction

Use the tangent ratio to find the steepness of a ramp, roof, or other incline when you know the vertical rise and horizontal run.

Example: A ramp with a rise of 2 ft and run of 10 ft has a tangent ratio of 0.2.

Frequently Asked Questions

What is the tangent ratio and how is it calculated?
The tangent ratio (tan) of an acute angle in a right triangle is the length of the side opposite the angle divided by the length of the side adjacent to it. This calculator does that division for you using the values you enter.
What units should I use for the opposite and adjacent sides?
You can use any consistent unit (e.g., inches, centimeters, feet) for both sides. The tangent ratio is dimensionless, so the units cancel out. Just ensure both values are in the same unit.
Can I use this calculator for any right triangle?
Yes, as long as you have the lengths of the side opposite and the side adjacent to the angle of interest. The calculator works for any right triangle, regardless of size.

Tips & Common Mistakes

Tips

  • Ensure both side lengths are in the same unit (e.g., both in meters) before entering them.
  • The tangent ratio is always a positive number for acute angles in a right triangle.
  • If you know the tangent ratio, you can find the angle using the inverse tangent (arctan) function on a scientific calculator.
  • Double-check that you have identified the correct opposite and adjacent sides relative to the angle you are working with.

Common Mistakes to Avoid

  • Mixing units (e.g., using meters for one side and centimeters for the other) without converting, which leads to an incorrect ratio.
  • Confusing the opposite and adjacent sides, especially when the triangle is rotated or the angle is not clearly marked.
  • Entering zero or a negative value for a side length, which is not valid for a real triangle.

Last updated: August 13, 2026