Exact
√3
Tan 60 Degrees
Answer
tan 60° equals √3, which is approximately 1.7320508076.
Decimal
1.7320508076
Formula
tan 60° = sin 60° / cos 60° = √3 ≈ 1.7320508076
Worked steps
1
From sin and cos
tan(angle) = sin(angle) / cos(angle). tan 60° = (√3/2) / (1/2) = √3.
2
Calculator method (DEG mode)
Set the calculator to DEG. Press tan, type 60, press =. Result: 1.7320508076.
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(1.7320508076) returns 60°.
About this value
Tan 60° = √3 is one of the standard tangent values memorised in trigonometry. At 60° the opposite side is √3 times the adjacent side. As angles approach 90°, tangent grows without bound — tan 90° is undefined.
Frequently asked questions
What is tan 60 degrees?
Tan 60 Degrees equals √3 as an exact value, or 1.7320508076 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 60° is 1.7320508076 in DEG or sin(angle_in_rad) of the equivalent radian measure.