Solve equations, simplify expressions, and compute trig values. Work in degrees or radians with results. Export results, compare examples, and learn formulas today fast.
| Tool | Example input | Expected output (rounded) |
|---|---|---|
| Quadratic solver | a=1, b=−3, c=2 | Roots: 1 and 2; Vertex: (1.5, −0.25) |
| 2×2 linear system | 2x + y = 5, x − y = 1 | x=2, y=1 |
| Polynomial eval + derivative | f(x)=x³−6x²+11x−6, x=2 | f(2)=0, f′(2)=3 |
| Trig values | θ=45° | sin≈0.7071, cos≈0.7071, tan≈1 |
| Angle converter | 180° → radians | π ≈ 3.1416 |
| Triangle (law of cosines) | a=7, b=9, C=60° | c≈8.185, Area≈27.279 |
The quadratic tool uses D = b² − 4ac to classify solutions. If D > 0, you get two real roots; if D = 0, one repeated real root; if D < 0, a complex conjugate pair. For example, a=1, b=−3, c=2 gives D=1 and roots 1 and 2.
Beyond roots, the calculator reports vertex location using xᵥ = −b/(2a) and yᵥ = f(xᵥ). This is useful for maxima and minima. With a=1, b=−3, c=2, the vertex is at xᵥ=1.5 and yᵥ=−0.25, and the axis of symmetry is x=1.5.
The 2×2 solver applies Cramer's rule. A unique solution exists only when D = a₁b₂ − b₁a₂ is nonzero. If D=0, lines are parallel or coincident, so there is no single (x, y) answer. Example: 2x+y=5 and x−y=1 yields D=−3, x=2, y=1.
Polynomial values are computed with Horner’s method, reducing operations and improving numerical stability. The derivative uses the power rule, turning aₖxᵏ into k·aₖxᵏ⁻¹. For f(x)=x³−6x²+11x−6 at x=2, the tool returns f(2)=0 and f′(2)=3, matching hand calculations.
Trigonometric functions in most computing libraries expect radians, so the calculator converts when you select degrees. The conversion is rad = deg·π/180. Common checkpoints: 180° equals π radians, 90° equals π/2, and 45° equals π/4. Switching units without converting is a frequent source of wrong results.
Some trig and reciprocal values become undefined when denominators approach zero. Tan(θ)=sin(θ)/cos(θ) becomes undefined near cos(θ)=0, such as 90° (π/2). Likewise, sec(θ)=1/cos(θ) and csc(θ)=1/sin(θ) can be undefined. The calculator shows a dash when a value cannot be safely computed.
Given sides a, b and included angle C, the triangle solver computes c using c² = a² + b² − 2ab·cos(C). It also estimates remaining angles and area using Area = ½ab·sin(C). Example: a=7, b=9, C=60° gives c≈8.185 and area≈27.279, which helps validate geometry and unit choices.
The decimals setting controls rounding in displayed results and exports. Higher precision is helpful for sensitive computations, like near-singular linear systems or trig angles close to undefined points. After you calculate, use the CSV export for spreadsheets and the PDF export for sharing. Exported tables include inputs, outputs, and optional steps for easy verification.
If D < 0, the quadratic has no real roots. The calculator shows two complex conjugate roots with the same real part and opposite imaginary parts.
When D = 0, the quadratic touches the x-axis once. Both roots are the same value (a repeated root), so it appears as a single solution conceptually.
It means the determinant D is zero. The equations represent parallel lines (no solution) or the same line (infinitely many solutions), so one exact (x, y) pair cannot be selected.
Tan depends on dividing by cos(θ). Near angles like 90° (π/2), cos(θ) approaches zero and tan grows without bound, so the calculator marks it as undefined.
Select the unit that matches your input. If you typed 45 expecting 45°, choose degrees. If your angle is π/4, choose radians. Mixing units is the most common trig mistake.
This tool supports degrees from 0 to 6 for a compact interface. If you need higher degrees, you can extend the coefficient inputs and reuse the same evaluation and derivative logic.
Exports include the selected tool name, rounded inputs, computed outputs, and the step list when enabled. This makes it easy to reproduce, audit, or share the calculation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.