πŸ“šStudyQuest

Formula Library

Browse, search, and interact with essential formulas across math and science. Tap any card to explore variables and try the built-in calculator.

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25 formulas found

algebra

Quadratic Formula

x=βˆ’bΒ±b2βˆ’4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Finds the roots of any quadratic equation axΒ² + bx + c = 0.

algebra

Slope-Intercept Form

y=mx+by = mx + b

The equation of a line where m is the slope and b is the y-intercept.

algebra

Point-Slope Form

yβˆ’y1=m(xβˆ’x1)y - y_1 = m(x - x_1)

Equation of a line using a known point (x₁, y₁) and the slope m.

algebra

Distance Formula

d=(x2βˆ’x1)2+(y2βˆ’y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Calculates the straight-line distance between two points on a coordinate plane.

algebra

Midpoint Formula

M=(x1+x22, y1+y22)M = \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}\right)

Finds the exact middle point between two coordinates.

algebra

Slope Formula

m=y2βˆ’y1x2βˆ’x1m = \frac{y_2 - y_1}{x_2 - x_1}

Calculates the slope (steepness) of a line between two points.

geometry

Area of a Circle

A=Ο€r2A = \pi r^2

Calculates the area enclosed by a circle with radius r.

geometry

Circumference of a Circle

C=2Ο€rC = 2\pi r

Calculates the perimeter (distance around) a circle.

geometry

Area of a Triangle

A=12bhA = \frac{1}{2}bh

Calculates the area of a triangle given its base and height.

geometry

Pythagorean Theorem

a2+b2=c2a^2 + b^2 = c^2

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

geometry

Volume of a Cylinder

V=Ο€r2hV = \pi r^2 h

Calculates the volume of a cylinder given its radius and height.

trigonometry

Sine (SOH)

sin⁑θ=oppositehypotenuse\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}

In a right triangle, sine of an angle equals the opposite side divided by the hypotenuse.

trigonometry

Cosine (CAH)

cos⁑θ=adjacenthypotenuse\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}

In a right triangle, cosine of an angle equals the adjacent side divided by the hypotenuse.

trigonometry

Tangent (TOA)

tan⁑θ=oppositeadjacent\tan\theta = \frac{\text{opposite}}{\text{adjacent}}

In a right triangle, tangent of an angle equals the opposite side divided by the adjacent side.

trigonometry

Pythagorean Identity

sin⁑2θ+cos⁑2θ=1\sin^2\theta + \cos^2\theta = 1

A fundamental trigonometric identity that holds true for all angles ΞΈ.

physics

Newton's Second Law

F=maF = ma

Force equals mass times acceleration β€” the foundation of classical mechanics.

physics

Velocity-Time Equation

v=v0+atv = v_0 + at

Calculates final velocity given initial velocity, acceleration, and time.

physics

Displacement Equation

d=v0t+12at2d = v_0 t + \frac{1}{2}at^2

Calculates displacement given initial velocity, acceleration, and time.

physics

Ohm's Law

V=IRV = IR

Voltage equals current times resistance in an electrical circuit.

physics

Work Formula

W=Fdcos⁑θW = Fd\cos\theta

Work equals force times displacement times the cosine of the angle between them.

chemistry

Ideal Gas Law

PV=nRTPV = nRT

Relates pressure, volume, amount, and temperature of an ideal gas.

chemistry

Density Formula

ρ=mV\rho = \frac{m}{V}

Density is mass per unit volume β€” how much matter is packed into a space.

chemistry

Mole Conversion

n=mMn = \frac{m}{M}

Converts between grams and moles using molar mass.

biology

Hardy-Weinberg Equation

p2+2pq+q2=1p^2 + 2pq + q^2 = 1

Predicts genotype frequencies in a non-evolving population. p and q are allele frequencies.

biology

Population Growth Rate

dNdt=rN\frac{dN}{dt} = rN

Exponential growth model where the rate of population change depends on the growth rate and current population size.