Solve triangles from common side-and-angle combinations, check valid inputs, and calculate area, perimeter, heights, medians, inradius, and circumradius in one place.
Calculates area from base and height. A unique triangle cannot be fully solved from these two values alone.
Enter triangle measurements to see results
Pick the method that matches your known values, enter the numbers with the right units, and let LiteCalc solve the triangle for you.
Use SSS for three known sides, SAS for two sides and the included angle, ASA for two angles and one side, or Base and Height when you only need area.
Type your lengths in centimeters, meters, inches, or feet. For angle-based tabs, you can choose degrees or radians before you calculate.
The results panel shows the missing sides, missing angles, area, perimeter, semiperimeter, heights, medians, inradius, and circumradius.
Base and height define area only, not one exact triangle. For a full triangle solution, use three valid measurements that include at least one side.
A solved triangle gives you more than side lengths. Each output tells you something practical about shape, size, and fit.
The side values describe the shape itself. If two sides match, the triangle may be isosceles. If all three sides match, it is equilateral. If all three sides are different, it is scalene. The angle values tell you whether the triangle is acute, right, or obtuse. That classification matters in design, drafting, trigonometry, and construction because some formulas or layout shortcuts are easier for right triangles than for oblique ones.
The area tells you how much two-dimensional space the triangle covers. The perimeter tells you the total distance around the outside. If you are estimating fencing, edging, trim, or material cuts, perimeter is usually the first number you need. If you are planning fabric, panel coverage, or sheet material usage, area is often the more important value.
The semiperimeter is half of the perimeter. It may look like a small extra detail, but it is central to Heron's formula and to inradius calculations. Heights, also called altitudes, show the perpendicular distance from a vertex to the opposite side. Each triangle has three altitudes because each side can act as a base.
A median runs from a vertex to the midpoint of the opposite side. Medians help describe balance points and are useful in geometry proofs. The inradius is the radius of the circle that fits inside the triangle and touches each side. The circumradius is the radius of the circle that passes through all three vertices. These values appear in engineering layouts, circle fits, and advanced geometry work.
If your inputs are rounded, your outputs will be rounded too. That is normal. In school settings, you may round to the nearest tenth or hundredth. In carpentry or shop work, you may round to the nearest eighth or sixteenth of an inch. If a fit is tight, keep more decimal places until the final step.
Suppose you know side a = 8 ft, side b = 11 ft, and the included angle C = 35 degrees. In SAS mode, the calculator first uses the law of cosines to find side c. Then it finds angles A and B, the perimeter, and the area. This is the kind of real-world setup you see when checking brace lengths, roof framing, or sign supports.
If you want to know how to calculate triangle values manually, these are the formulas behind the calculator.
When you know all three side lengths, the area comes from Heron's formula. First calculate the semiperimeter: s = (a + b + c) / 2. Then calculate area with A = sqrt(s(s-a)(s-b)(s-c)). To find the missing angles, use the law of cosines. For angle A, the formula is cos A = (b^2 + c^2 - a^2) / 2bc. The same pattern works for angles B and C.
In SAS problems, the missing side is found first with the law of cosines: c^2 = a^2 + b^2 - 2ab cos C. Once you know the third side, you can solve the other angles and compute the area. A quick area formula for SAS is A = 1/2 ab sin C. This is one of the most useful manual triangle formulas because it avoids extra steps when two sides and an included angle are already known.
In ASA or AAS problems, begin with the angle sum rule: A + B + C = 180 degrees. Once you know the third angle, use the law of sines: a / sin A = b / sin B = c / sin C. This lets you scale the triangle from one known side to the other two. The law of sines is especially helpful when your drawing gives you angle information more clearly than side information.
Perimeter is a + b + c. Each altitude is h = 2A / side. Each median comes from a side-based formula such as m_a = 1/2 sqrt(2b^2 + 2c^2 - a^2). Inradius is r = A / s, where s is the semiperimeter. Circumradius is R = abc / 4A. These are the semantically related terms you often see in geometry texts: altitude, median, semiperimeter, inradius, circumradius, law of sines, and law of cosines.
Real triangle problems show up in school, construction, design, surveying, and DIY planning. These examples show how to think about the inputs.
You measure two rafters at 9 ft and 12 ft with an included angle of 48 degrees. SAS mode gives the third side, area, and the remaining angles. This helps when you want to cut a brace or estimate the opening between members.
A triangular planting bed has sides of 6 ft, 7 ft, and 9 ft. SSS mode uses Heron's formula to find area, which helps estimate mulch, edging, or weed barrier without drawing the shape to scale.
Suppose a portable ramp uses two sides of 1.0 m and 0.8 m, with an included angle of 85 degrees. The calculator finds the third side and altitude quickly, which tells you if the rise fits your doorway or trailer.
If your worksheet gives angles A = 38 degrees and B = 71 degrees with side c = 14 cm, ASA mode finds the third angle and the missing sides. That makes it easy to verify notebook work before turning in an assignment.
A field crew may know two measured distances and one angle from a station point. Solving the triangle helps estimate the third distance before staking or marking a boundary line, saving time and repeated measuring.
When you cut a triangular gusset or decorative panel, area helps estimate material waste while perimeter helps estimate trim or edge banding. If you work in the US, entering feet and inches is often easier than converting first.
Imagine you are checking a triangular support bracket with side a = 8 in, side b = 13 in, and side c = 15 in. In SSS mode, the calculator first finds semiperimeter: s = (8 + 13 + 15) / 2 = 18. Then it applies Heron's formula: A = sqrt(18 x 10 x 5 x 3) = sqrt(2700) ? 51.96 in?.
The perimeter is 36 in. The altitude to side c is h_c = 2A / c ? 6.93 in. From there, the calculator also finds each angle with the law of cosines and reports the inradius and circumradius. This is a practical example because one set of side measurements answers questions about fit, material area, and layout all at once.
One of the biggest content gaps on many calculator pages is input validation. Knowing the rules helps you avoid impossible triangles and confusing results.
If you enter three sides, the sum of any two sides must be greater than the third. For example, 2, 3, and 6 cannot form a triangle because 2 + 3 is not greater than 6. The calculator checks this rule before solving.
The interior angles of a triangle always add to 180 degrees. In ASA and AAS situations, the known angles must add to less than 180 degrees so there is room for the third angle. If they do not, the inputs are not valid.
SSS, SAS, ASA, and AAS usually produce one unique triangle. Base and height do not. That is why the base-and-height tab returns area only. Many different triangles can share the same base and perpendicular height.
Another important limit is the ambiguous case, often called SSA. In SSA, you know two sides and a non-included angle. Depending on the values, there can be no triangle, one triangle, or two valid triangles. Several high-ranking competitors explain this case because it is one of the most common reasons students and DIY users get stuck. LiteCalc's current widget focuses on the safest common modes, but it helps to understand why some measurement sets are less direct than others.
Unit consistency matters too. Mixing centimeters, feet, and inches is fine as long as the calculator converts them before solving. Angles are different because they need a clear mode. If you type a radian value but treat it like degrees, the shape will be wrong. That is why the angle boxes support either degrees or radians. When you choose radians, enter the numeric radian value and let the calculator translate it internally.
Finally, remember that measurements from real objects include error. If you are working from tape measurements, blueprints, or field notes, a small difference in one angle can shift every other output. For exact academic work, use the most precise values you have. For practical field work, compare the solved triangle to your tolerance for cutting, fitting, or staking before treating the result as final.
Keep solving related geometry problems with other free LiteCalc tools.
Use our right triangle calculator to solve Pythagorean theorem problems, special right triangles, and slope-style geometry.
Compare triangle area with other shapes using our area calculator for rectangles, circles, trapezoids, and more.
Convert 2D thinking into 3D estimates with formulas for prisms, cylinders, cones, and other solids.
Simplify ratios, side lengths, and classroom math with our fraction calculator when your triangle values are not decimals.
Work with similar triangles, scale drawings, and proportional side relationships using our ratio calculator.
Calculate weighted values for grades, scores, and mixed data when your geometry work leads into broader math problems.
These answers cover the triangle questions people search most often before using a side and angle calculator.
You can solve a triangle when you know any three valid measurements and at least one of them is a side. In most cases, that means SSS, SAS, ASA, or AAS. The calculator applies the law of cosines, the law of sines, Heron's formula, and the angle sum rule to fill in the missing values.
Yes. The angle inputs can be interpreted in degrees or radians. If you select radians, the calculator converts the values before solving the triangle. That makes the tool useful for both basic geometry and more advanced trigonometry work.
Use Heron's formula. First find the semiperimeter, s = (a + b + c) / 2. Then calculate area = sqrt(s(s-a)(s-b)(s-c)). This is the standard formula for an SSS triangle when all side lengths are known.
Check the triangle inequality for side inputs and the angle sum rule for angle inputs. The sum of any two sides must be greater than the third side, and the interior angles must total 180 degrees. If either rule fails, the triangle is impossible.
The semiperimeter is half the perimeter. If the three sides are a, b, and c, then s = (a + b + c) / 2. It is used in Heron's formula and in the inradius formula r = A / s.
Use the law of cosines when you know all three sides. Use the law of sines when you know a side-angle pair and another side or angle. In ASA and AAS problems, you can often find the third angle first by subtracting the two known angles from 180 degrees.
Yes. Once you know the area, the altitude to any side can be found with h = 2A / side. For example, if side c is the base, then h_c = 2A / c. This is one of the fastest ways to compute a triangle height from SSS results.
The ambiguous case appears in SSA problems, where you know two sides and a non-included angle. Depending on the values, there may be no triangle, one triangle, or two possible triangles. That is why SSA is less straightforward than SSS, SAS, or ASA.