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Input fractions, surds, decimals → Get exact symbolic results

Try inputs like: 1/2,sqrt(2),3*pi,2 1/4

15 equations found

Geometry

A = \pi r^2

Calculate circle area with exact π expressions

Electronics

C = \frac{Q}{V}

Find any of the variables in the standard equation for capacitance

Finance

A = P\left(1 + \frac{r}{n}\right)^{nt}

Calculate compound interest with principal, rate, compounding frequency and time

Geometry

c^2 = a^2 + b^2 - 2ab\cos(C)

Find any side or angle in a triangle using the cosine rule

Electronics

V = I \cdot R

Relationship between voltage, current, and resistance

Physics

hf = \Phi + KE_{max}

Find variables in the photoelectric equation relating photon energy to work function and kinetic energy

Electronics

V_{out} = \frac{R_2}{R_1 + R_2} \times V_{in}

Calculate output voltage in a two-resistor potential divider circuit

Geometry

c^2 = a^2 + b^2

Calculate triangle sides with exact surd results

Algebra

ax^2 + bx + c = 0 \Rightarrow x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Solves quadratic equations with exact symbolic results including combined surds and fractions

Electronics

\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2}

Calculate total resistance of two resistors in parallel

Physics

n_1 \sin(\theta_1) = n_2 \sin(\theta_2)

Find any variable in Snells Law relating refractive indices and angles

Physics

v = u + at \quad s = ut + \frac{1}{2}at^2 \quad v^2 = u^2 + 2as

Uniformly accelerated motion equations - finds any 2 missing variables when 3 are provided

Trigonometry

\sin^2(\theta) + \cos^2(\theta) = 1

Calculate exact trigonometric values for common angles

Geometry

V = \frac{4}{3}\pi r^3

Calculate sphere volume with exact π expressions

Physics

v = f \lambda

Find any variable in the wave equation relating velocity, frequency, and wavelength