Mathematics

Calculate parts per million (ppm = mass of solute ÷ mass of solution × 1,000,000) and the equivalent percentage from a solute mass and a solution mass.

Calculate pressure from force and area — pressure = force ÷ area, in pascals (Pa).

Convert pressure between pascal, bar, atmosphere, psi, mmHg, and more — instantly and with exact, pascal-based conversion factors.

Calculate the price elasticity of demand with the midpoint method and see whether demand is elastic, inelastic, or unit elastic.

Decompose any whole number from 2 to 1,000,000,000 into its unique prime factors in exponent form — for example 360 into 2^3 multiplied by 3^2 multiplied by 5.

Calculate the maximum height of a projectile (h = v²·sin²θ / 2g) from its initial velocity and launch angle, ignoring air resistance.

Calculate the horizontal range of a projectile on level ground (R = v² × sin(2θ) / g) from its launch speed and angle, ignoring air resistance.

Calculate the time of flight, horizontal range, and maximum height of a projectile launched from ground level — time = 2v·sinθ/g, range = v²·sin(2θ)/g, height = v²·sin²θ/(2g).

Calculate the volume, lateral surface, and total surface area of a square pyramid frustum from its bottom side, top side, and height — volume = (h/3)(a² + ab + b²).

Calculate the total and lateral surface area of a square pyramid from its base edge and slant height — total = b² + 2bl, lateral = 2bl.

Calculate the volume, base area, and slant height of a square pyramid from its base edge and height — volume = (1/3)a²h, base area = a², slant height = √(h²+(a/2)²).

Find the hypotenuse, area, and perimeter of a right triangle from its two legs using the Pythagorean theorem: c = √(a² + b²).

Solve any quadratic equation ax² + bx + c = 0 for its real roots and see the discriminant that tells you how many real solutions exist.

Calculate the area, perimeter, and arc length of a quarter circle from its radius — area = ¼πr², arc length = ½πr, perimeter = ½πr + 2r.

Calculate how much of a radioactive substance is left after decay with N = N0 × (1/2)^(elapsed / half-life), from the initial amount, elapsed years, and half-life.

Solve a proportion A : B = C : D for the missing value and reduce the ratio A : B to its simplest whole-number form.

Calculate the cutoff frequency and time constant of a first-order RC high-pass filter from its resistance and capacitance — f_c = 1 / (2π × R × C).

Calculate the cutoff frequency and time constant of a first-order RC low-pass filter from its resistance and capacitance — f_c = 1 / (2π × R × C).

Calculate the time constant of an RC circuit — τ = R × C — the time it takes to charge to ~63 % or discharge to ~37 % of the final voltage.

Estimate how long a text takes to read from its word count and your reading speed, shown in minutes and seconds.

Work out what a run of reinforcing bar weighs — for a bar schedule, a delivery note or a lift.

Calculate the area, perimeter, and diagonal of a rectangle from its length and width — area = L×W, perimeter = 2(L+W), diagonal = √(L²+W²).

Calculate the volume, surface area, and space diagonal of a rectangular prism (box) from its length, width, and height — volume = l×w×h, surface area = 2(lw+lh+wh), diagonal = √(l²+w²+h²).

Calculate the redshift z = (λ_observed − λ_rest) / λ_rest of a spectral line and the low-redshift recession velocity of a galaxy from its wavelengths.

Calculate the refractive index (n = c / v) of a medium from the speed of light within it, using the exact speed of light in vacuum.

Calculate the volume and surface area of a regular dodecahedron from its edge length — volume = ((15+7√5)/4)·a³, surface area = 3√(25+10√5)·a².

Calculate the volume and surface area of a regular icosahedron from its edge length — volume = (5(3+√5)/12)·a³, surface area = 5√3·a².

Calculate the volume and surface area of a regular octahedron from its edge length — volume = (√2/3)·a³, surface area = 2√3·a².

Calculate the area, perimeter, and apothem of a regular polygon from its number of sides and side length — area = ½ × perimeter × apothem, apothem = s/(2·tan(π/n)).

Calculate the volume, surface area, and height of a regular tetrahedron from its edge length — volume = a³/(6√2), surface area = √3·a², height = a·√(2/3).

Calculate the magnitude of the resultant of two forces acting at an angle using R = √(F1² + F2² + 2·F1·F2·cosθ).

Calculate a room's Sabine reverberation time (RT60) and total absorption from its volume, surface area, and average absorption coefficient — RT60 = 0.161·V/A, A = S·α.

Find the original value before a percentage increase or decrease, or work out what number a value is a given percentage of.

Calculate the Reynolds number (Re = ρvL/μ) from fluid density, velocity, characteristic length, and dynamic viscosity, and see whether the flow is laminar or turbulent.

Calculate the area, side length, and perimeter of a rhombus from its two diagonals — area = (d1 × d2) ÷ 2.

Calculate the hypotenuse, area, perimeter, and acute angles of a right triangle from its two legs — hypotenuse = √(a²+b²), area = ½ab, angles via atan.

Convert a ring's inner diameter in millimetres to US and EU/ISO ring sizes, with the inner circumference shown alongside.

Calculate the time constant of an RL (resistor–inductor) circuit from its inductance and resistance — τ = L / R — plus the time to reach steady state.

Calculate the RMS voltage (V_rms = V_peak / √2) and peak-to-peak voltage of a sine wave from its peak voltage (amplitude).

Calculate the road or slope grade as a percentage ((rise / run) × 100) and the slope angle in degrees from a vertical rise and a horizontal run.

Calculate the change in velocity (Δv = ve · ln(m0/mf)) of a rocket from its exhaust velocity and its wet and dry mass using the Tsiolkovsky rocket equation.

Convert any whole number from 1 to 3999 into its standard Roman numeral, using the subtractive notation (IV, IX, XL, XC, CD, CM).

Solve for the unknown value in a proportion using the rule of three (Dreisatz), with support for both direct and inverse relationships.

Calculate the wavelength of a hydrogen spectral line with the Rydberg equation (1/λ = R·(1/n1² − 1/n2²)) from the two principal quantum numbers.

Calculate your total SAT score from the Math and Reading & Writing (EBRW) section scores and see the national percentile rank.

Convert a measured model or map length into the real-world length for any 1:N scale, plus the reverse scaled-down length.

Calculate the Schwarzschild radius (event horizon) r_s = 2GM/c² of any mass in metres and kilometres — the radius at which it would become a black hole.

Convert any decimal number into scientific notation — a coefficient between 1 and 10 multiplied by a power of ten — and read off the mantissa and exponent.

Calculate the physical width and height of a screen from its diagonal size and aspect ratio (16:9, 4:3, 21:9) in the same unit as the diagonal.

Calculate the area, perimeter, arc length, and diameter of a semicircle from its radius — area = ½πr², perimeter = πr + 2r, arc = πr.