Law of Sines Calculator
Solve triangles from angles and a side.
Enter your values
Enter the angle a in degrees.
Enter the angle b in degrees.
Enter the side a (opposite a) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Side b
- 14.09965
- Side c
- 15.02714
- Angle C
- 75°
- Area
- 68.09606
- Circumradius
- 7.77862
Quick answer
The law of sines states that each side divided by the sine of its opposite angle is the same constant.
a/sin A = b/sin B = c/sin C
At a glance
| What it does | Solve triangles from angles and a side. |
|---|---|
| Category | Math |
| Inputs needed | Angle A, Angle B, Side a (opposite A) |
| Main output | Side b |
| Formula | a/sin A = b/sin B = c/sin C |
| Cost | Free — no sign-up, no download |
How to use the Law of Sines Calculator
- 1Enter two known angles in degrees.
- 2Enter the side opposite the first angle.
- 3Read the remaining sides and angle.
Inputs explained
- Angle A(degrees)
- Enter the angle a in degrees.
- Angle B(degrees)
- Enter the angle b in degrees.
- Side a (opposite A)
- Enter the side a (opposite a) you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Angle A40 degrees
- Angle B65 degrees
- Side a (opposite A)10
Results
- Side b14.09965
- Side c15.02714
- Angle C75°
- Area68.09606
- Circumradius7.77862
Frequently asked questions
What is the ambiguous case?
With two sides and a non-included angle, there may be two valid triangles.
What is the circumradius?
Half the common ratio a/sin A — the radius of the circle through all three vertices.
What do I need to enter into the Law of Sines Calculator?
Just 3 values: angle a, angle b, side a (opposite a). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Law of Sines Calculator work out the answer?
The law of sines states that each side divided by the sine of its opposite angle is the same constant. It applies the formula a/sin A = b/sin B = c/sin C and shows the working so you can check each step by hand.
Is the Law of Sines Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.