Exact
√2/2
Sin 45 Degrees
Answer
sin 45° equals √2/2, which is 0.7071067812 as a decimal.
Decimal
0.7071067812
Formula
sin 45° = √2/2 ≈ 0.7071067812
Worked steps
1
Right-triangle definition
In a right triangle, sin(angle) = opposite side ÷ hypotenuse. For a 30°–60°–90° triangle with sides 1 : √3 : 2, the side opposite the 45° angle gives sin 45° = √2/2.
2
Calculator method (DEG mode)
Set the calculator to DEG. Press sin, type 45, press =. Result: 0.7071067812.
3
Calculator method (RAD mode)
Convert 45° to radians first: 45 × π / 180 = 0.785398 rad. Then sin of that gives 0.7071067812.
About this value
Sin 45° is one of the standard angle values memorised in trigonometry. The exact form is √2/2, and the decimal 0.7071067812 is what a scientific calculator returns. This is the value at the diagonal of a unit square — sin 45° = cos 45° = √2/2.
Frequently asked questions
What is sin 45 degrees?
Sin 45 Degrees equals √2/2 as an exact value, or 0.7071067812 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 sin, 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 45° is 0.7071067812 in DEG or sin(angle_in_rad) of the equivalent radian measure.