Exact
1/√3
Tan 30 Degrees
Answer
tan 30° equals 1/√3, which is approximately 0.5773502692.
Decimal
0.5773502692
Formula
tan 30° = sin 30° / cos 30° = 1/√3 ≈ 0.5773502692
Worked steps
1
From sin and cos
tan(angle) = sin(angle) / cos(angle). tan 30° = (1/2) / (√3/2) = 1/√3 = √3/3.
2
Calculator method (DEG mode)
Set the calculator to DEG. Press tan, type 30, press =. Result: 0.5773502692.
3
Inverse check
To go back from a tangent value to the angle, use tan⁻¹ (or arctan). On the calculator in DEG mode, tan⁻¹(0.5773502692) returns 30°.
About this value
Tan 30° = 1/√3 is one of the standard tangent values memorised in trigonometry. At 30°, tan equals one over √3, sometimes written √3/3 after rationalising the denominator.
Frequently asked questions
What is tan 30 degrees?
Tan 30 Degrees equals 1/√3 as an exact value, or 0.5773502692 as a decimal. The exact form is what you'd typically write in exam working; the decimal is what your calculator displays.
How do I enter this on a calculator?
Set the angle mode to DEG. Press tan, type the angle, press =. If your calculator is in RAD mode by mistake, you will get a different answer — always check the mode pill before pressing a trig function.
Why memorise the standard angle values?
The values for 30°, 45°, 60°, and 90° appear in almost every trigonometry problem at school level. Knowing the exact form (with surds) lets you produce surd-form answers expected in exams, instead of decimal approximations.
What is this in radians?
To convert the angle to radians, multiply by π/180. The function value is the same regardless of mode — the answer for 30° is 0.5773502692 in DEG or sin(angle_in_rad) of the equivalent radian measure.