Triangle Calculator
What are the area and angles of a triangle when I know its three sides? Enter the values below to calculate the result.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Side a (length) | Enter side a in length; use the same basis as the other measurements. |
| Side b (length) | Enter side b in length; use the same basis as the other measurements. |
| Side c (length) | Enter side c in length; use the same basis as the other measurements. |
Understanding your result
Read area (length^2), perimeter (length), A (degree), B (degree), C (degree) in the units and model stated on this page. The formula s=(a+b+c)/2 · area=sqrt(s*(s-a)*(s-b)*(s-c)) · perimeter=2*s · A=acos(min(1,max(-1,(b*b+c*c-a*a)/(2*b*c))))*180/pi · B=acos(min(1,max(-1,(a*a+c*c-b*b)/(2*a*c))))*180/pi · C=180-A-B defines the relationship; measurement accuracy and model applicability are separate from numerical precision.
Common mistakes
- Mixing input units or changing the physical meaning of a variable without changing the model.
Check your calculation
- Use the worked example as a known reference case, then change one input at a time and check the direction and units of the response.
Calculation checks, sources and review limits
What are the area and angles of a triangle when I know its three sides?
What are the area and angles of a triangle when I know its three sides? Enter the values below to calculate the result.
Common uses
- What are the area and angles of a triangle when I know its three sides
How it works
s=(a+b+c)/2; area=sqrt(s*(s-a)*(s-b)*(s-c)); perimeter=2*s; A=acos(min(1,max(-1,(b*b+c*c-a*a)/(2*b*c))))*180/pi; B=acos(min(1,max(-1,(a*a+c*c-b*b)/(2*a*c))))*180/pi; C=180-A-B
Worked example
Enter Side a: 3 length; Side b: 4 length; Side c: 5 length. Results: area: 6 length^2; perimeter: 12 length; A: 36.869897645844 degree; B: 53.130102354156 degree; C: 90 degree.