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Scientific & Math Calculators

This group covers the maths that goes beyond arithmetic: functions, geometry and the summary statistics behind a data set. Students, teachers, lab technicians and anyone checking a spreadsheet formula by hand are the people who need them. The Scientific Calculator is the general instrument, with trigonometric functions, logarithms, exponents, roots, constants and bracketed expressions evaluated in the proper order. It replaces a handheld unit for homework and quick checks, and it is the right place to start when your problem is an expression rather than a shape or a sample. The Triangle Calculator solves for the missing sides and angles once you supply enough known values, applying the sine and cosine rules and returning area and perimeter along the way. That saves choosing the right identity yourself, and it suits geometry coursework, surveying sketches and anything involving a sloped measurement. The Statistics Calculator takes a list of numbers and reports mean, median, mode, range, variance and standard deviation together, which is more useful than a single figure because the spread usually matters as much as the centre. Paste readings straight from a table and read the summary off in one pass. All three calculate in your browser, with no sign-up and nothing sent to a server.

3 tools available

Showing 1–3 of 3

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Scientific Calculator

Full scientific calculator with trigonometry, logs, powers, roots, factorials and a running history.

Scientific & Math Calculators 203 uses
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Statistics Calculator

Compute mean, median, mode, quartiles, IQR, variance, standard deviation and skewness from a pasted list of numbers.

Scientific & Math Calculators 485 uses
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Triangle Calculator

Solve a triangle from any three known sides or angles and get every remaining measurement.

Scientific & Math Calculators 342 uses

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Sine rule, cosine rule and the derived quantities

Two relationships do most of the work. The cosine rule says c squared equals a squared plus b squared minus twice a times b times the cosine of angle C, which solves SSS and SAS. The sine rule states that a divided by the sine of A equals b divided by the sine of B equals c divided by the sine of C, and that common value equals twice the circumradius. That handles ASA, AAS and SSA, and the angles always sum to 180 degrees, supplying the third once two are known.

Area comes from half of a times b times the sine of the included angle, or from Heron's formula when only the sides are known. From the area the rest follows. Each altitude is twice the area divided by the side it meets. The inradius is the area divided by the semi-perimeter. The circumradius is the product of the three sides divided by four times the area. The median to side a is half the square root of twice b squared plus twice c squared minus a squared.

Classification follows: equal sides give equilateral or isosceles, and the largest angle decides acute, right or obtuse.

Worked example: two sides of 8 and 6 with a 60 degree angle between them

Take the SAS case with side a of 8, side b of 6 and the included angle C of 60 degrees.

The cosine rule gives c squared as 64 plus 36 minus 2 times 8 times 6 times the cosine of 60 degrees. The cosine of 60 is 0.5, so the last term is 48, leaving c squared as 52 and c as 7.211.

The area is half of 8 times 6 times the sine of 60 degrees, which is 24 multiplied by 0.8660, giving 20.78. The perimeter is 8 plus 6 plus 7.211, or 21.211, so the semi-perimeter is 10.606.

For the remaining angles, the sine rule gives the sine of A as 8 times 0.8660 divided by 7.211, which is 0.9608, so angle A is 73.90 degrees. Angle B is then 180 minus 60 minus 73.90, or 46.10 degrees.

The derived values follow: the inradius is 20.78 divided by 10.606, which is 1.959, and the circumradius is 8 times 6 times 7.211 divided by four times 20.78, which is 346.1 divided by 83.14, or 4.164. All three sides differ and the largest angle is under 90 degrees, so this is a scalene acute triangle.

The ambiguous case and other places solutions break down

SSA is the only input combination that can describe two different triangles, and the calculator flags this explicitly and shows the second solution when one exists. It arises when the known angle is acute and the side opposite it is shorter than the adjacent side but longer than the perpendicular height to the base. Both the acute and the obtuse value of the unknown angle then satisfy the sine rule. If you have a sketch or a physical constraint, use it to decide which is yours; the arithmetic alone cannot.

Some inputs describe no triangle at all. Three sides must satisfy the triangle inequality, meaning any two added together exceed the third, so 3, 4 and 9 is impossible. Two angles must total less than 180 degrees, leaving room for the third. Very thin triangles, where one angle approaches zero or 180 degrees, are valid but sensitive, and a small error in a measured side can swing the computed angles noticeably.

Results are rounded for display, so recomputing from the rounded outputs may drift slightly from the original inputs. Where a drawing or a cut must be accurate, work from the values you measured rather than from a rounded intermediate.

Frequently Asked Questions

Three, and at least one must be a side. Three angles fix the shape but not the size, so any triangle with those angles is a valid answer. The supported combinations are SSS, SAS, ASA, AAS and SSA, plus several right-triangle shortcuts using two legs, a leg and the hypotenuse, or a side with an acute angle.
When you know two sides and an angle that is not between them, two different triangles can sometimes satisfy the same measurements, one acute and one obtuse at the unknown angle. The calculator detects this, warns you, and displays the second solution with its own angles, area and perimeter so you can pick the right one.
The inradius is the radius of the largest circle that fits inside the triangle, touching all three sides, and equals the area divided by the semi-perimeter. The circumradius is the radius of the circle passing through all three vertices, equal to the product of the sides divided by four times the area. Both are common in geometry and layout work.
Most often because the three sides break the triangle inequality: any two sides added together must be longer than the third, so 3, 4 and 9 cannot close. The other common cause is two angles that already total 180 degrees or more, leaving nothing for the third angle.
Both. You enter angles in degrees, and each result is displayed in degrees with the radian equivalent underneath, so the same solution works for trigonometry coursework that requires radians and for practical work that uses degrees. The sector and area formulas convert internally wherever radians are required.