Online Calculators FreeReference Manual

Advanced Math Calculator

The math past the basics in one dropdown: triangle solvers (SSS, SAS, ASA), law of sines and cosines, determinants, inverses and matrix products, vector dot and cross products, arithmetic and geometric series, Fibonacci, base conversion, Roman numerals, two’s complement, bitwise logic, complex numbers, and polar coordinates.

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CalculatorFORM ADVANCED MATH CALCULATOR
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One page, the whole second course

Pick the topic from the dropdown and the form adapts: three sides for the SSS triangle solver, two angle fields for the law of sines, semicolon-separated rows for matrices, a single comma-separated field for vectors. Every member shows the substituted formula beneath the board, so each answer doubles as a worked example.

The formulas at a glance

Triangles: cos C = (a² + b² − c²)/(2ab), a/sin A = b/sin B, shoelace ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|. Matrices: det = ad − bc, inverse = adjugate ÷ determinant. Vectors: u·w = |u||w|cos θ; u×w is perpendicular to both. Series: aₙ = a₁ + (n−1)d, Sₙ = n(a₁+aₙ)/2, and S = a₁/(1−r) only when |r| < 1. Numbers: two's complement = flip the bits and add one.

Worked example

  1. Solve a 3-4-5 triangle with the SSS member.
  2. Enter sides 3, 4, 5 — the inequality check passes.
  3. cos C = (9 + 16 − 25)/24 = 0, so C = 90° exactly.
  4. The board also lists A ≈ 36.87°, B ≈ 53.13°, area 6, and perimeter 12.

How to use it

  1. Choose the topic from the dropdown — triangles, matrices, vectors, sequences, number systems, complex numbers, or coordinates.
  2. Fill the fields; matrices and vectors go in as comma-separated numbers with rows split by semicolons.
  3. Read the result, the extra rows, and the substituted formula beneath the board.
  4. Copy, print, or share the link — it remembers the member and your values.

Frequently asked questions

How do I find the angles of a triangle from three sides?

Use the SSS member: the law of cosines gives each angle as cos⁻¹((b²+c²−a²)/(2bc)). The 3-4-5 triangle returns 36.87°, 53.13°, and 90°, and the tool refuses side lengths that violate the triangle inequality.

When does the law of sines give two different triangles?

Only in the SSA case (two sides and a non-included angle), where an acute and an obtuse solution can both fit. This tool asks for two angles plus a side (ASA/AAS), which always has a unique answer.

Why did my matrix inverse fail?

The determinant was zero, so the matrix is singular — its rows are multiples of each other and no inverse exists. Change one row (or use the determinant member first to check).

Why must the ratio be less than 1 for an infinite geometric series?

The sum S = a₁/(1−r) only converges when the terms shrink, i.e. |r| < 1. With a₁ = 1 and r = 0.5 the sum is exactly 2; with r = 2 it grows forever, and the tool says so.

What is two’s complement used for?

It is how hardware stores negative integers: flip every bit of the positive pattern and add one. In 8 bits, 5 is 00000101, so −5 is 11111011. The member shows both patterns for any width from 2 to 64 bits.

Why do Roman numerals stop at 3,999?

Standard subtractive notation has no symbol beyond M (1,000) and allows at most three in a row, so MMMCMXCIX = 3,999 is the ceiling. The converter rejects non-standard forms like IIII or VX and explains why.