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209 results for “met”

Formulae (204)

Percentage

\% = \frac{\text{part}}{\text{whole}} \times 100

What fraction of a whole a part represents, out of 100.

Arithmetic & BasicsBasic

Percent of a Number

\text{value} = \frac{p}{100} \times N

Find p percent of a number N.

Arithmetic & BasicsBasic

Percentage Change

\% \text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100

Increase or decrease of a value as a percentage.

Arithmetic & BasicsBasic

Fraction to Decimal

\frac{a}{b} = a \div b

Convert a fraction into a decimal by dividing.

Arithmetic & BasicsBasic

Adding Fractions

\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}

Add two fractions using a common denominator.

Arithmetic & BasicsBasic

Multiplying Fractions

\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

Multiply numerators and denominators straight across.

Arithmetic & BasicsBasic

Dividing Fractions

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Divide by multiplying by the reciprocal (flip and multiply).

Arithmetic & BasicsBasic

Average (Mean)

\text{average} = \frac{\text{sum of values}}{\text{number of values}}

Add all values and divide by how many there are.

Arithmetic & BasicsBasic

Ratio

a : b = \frac{a}{b}

Compares two quantities by division.

Arithmetic & BasicsBasic

Proportion (Cross Multiply)

\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc

Two equal ratios; solve using cross multiplication.

Arithmetic & BasicsBasic

Unit Rate

\text{unit rate} = \frac{\text{total}}{\text{quantity}}

Cost or amount for a single unit.

Arithmetic & BasicsBasic

Speed = Distance ÷ Time

s = \frac{d}{t}

How fast something moves.

Arithmetic & BasicsBasic

Distance = Speed × Time

d = s \times t

How far something travels.

Arithmetic & BasicsBasic

Rounding Rule

5\text{ or more} \uparrow, \ 4\text{ or less} \downarrow

Round up if the next digit is 5+, otherwise round down.

Arithmetic & BasicsBasic

Order of Operations (PEMDAS)

P \to E \to (M \div D) \to (A \div S)

Parentheses, Exponents, Multiply/Divide, Add/Subtract.

Arithmetic & BasicsBasic

Place Value

N = \sum d_i \times 10^{i}

Each digit’s value depends on its position.

Arithmetic & BasicsBasic

Even and Odd

n \bmod 2 = 0 \Rightarrow \text{even}

A number is even if it divides by 2 with no remainder.

Arithmetic & BasicsBasic

Discount Price

\text{price} = N \left(1 - \frac{p}{100}\right)

Final price after a percentage discount.

Arithmetic & BasicsBasic

Sales Tax Total

\text{total} = N \left(1 + \frac{t}{100}\right)

Price after adding a percentage tax.

Arithmetic & BasicsBasic

Tip Amount

\text{tip} = \frac{p}{100} \times \text{bill}

Gratuity as a percentage of the bill.

Arithmetic & BasicsBasic

Percent Increase

new = old(1 + p)

Value after a percentage increase.

Arithmetic & BasicsBasic

Percent Decrease

new = old(1 - p)

Value after a percentage decrease.

Arithmetic & BasicsBasic

Mixed Number to Fraction

a\frac{b}{c} = \frac{ac + b}{c}

Convert a mixed number to an improper fraction.

Arithmetic & BasicsBasic

Reciprocal

\frac{1}{x}

The multiplicative inverse of a number.

Arithmetic & BasicsBasic

Square of a Number

n^2 = n\times n

A number multiplied by itself.

Arithmetic & BasicsBasic

Cube of a Number

n^3 = n\times n\times n

A number multiplied by itself three times.

Arithmetic & BasicsBasic

Square Root

\sqrt{n}

The value that squares to n.

Arithmetic & BasicsBasic

Divisibility by 3

\text{digit sum divisible by 3}

A number is divisible by 3 if its digit sum is.

Arithmetic & BasicsBasic

Divisibility by 9

\text{digit sum divisible by 9}

A number is divisible by 9 if its digit sum is.

Arithmetic & BasicsBasic

Percent to Fraction

p\% = \frac{p}{100}

Convert a percentage to a fraction.

AlgebraBasic

Arithmetic Series Sum

S_n = \frac{n}{2}(a_1 + a_n)

Sum of the first n terms of an arithmetic sequence.

AlgebraBasic

Arithmetic nth Term

a_n = a_1 + (n-1)d

The nth term of an arithmetic sequence.

AlgebraIntermediate

Geometric Series Sum

S_n = a_1 \frac{1 - r^n}{1 - r}

Sum of the first n terms of a geometric sequence (r ≠ 1).

AlgebraIntermediate

Infinite Geometric Series

S = \frac{a_1}{1 - r}, \quad |r| < 1

Sum of an infinite geometric series that converges.

AlgebraBasic

FOIL Method

(a+b)(c+d) = ac + ad + bc + bd

Multiply two binomials: First, Outer, Inner, Last.

AlgebraIntermediate

Geometric Mean

GM = \sqrt[n]{x_1 x_2 \cdots x_n}

The nth root of the product of n numbers.

AlgebraAdvanced

Infinite Geometric Series

S = \frac{a}{1-r}, \; |r|<1

Sum of an infinite geometric series that converges.

AlgebraIntermediate

Finite Geometric Series

S_n = a\frac{1-r^n}{1-r}

Sum of the first n terms of a geometric series.

Geometry & TrigonometryBasic

Pythagorean Theorem

a^2 + b^2 = c^2

Relates the sides of a right triangle.

Geometry & TrigonometryBasic

Area of a Circle

A = \pi r^2

The area enclosed by a circle.

Geometry & TrigonometryBasic

Circumference of a Circle

C = 2\pi r

The perimeter (boundary length) of a circle.

Geometry & TrigonometryBasic

Area of a Rectangle

A = l \times w

Area of a rectangle.

Geometry & TrigonometryBasic

Area of a Triangle

A = \frac{1}{2} b h

Area of a triangle from base and height.

Geometry & TrigonometryBasic

Area of a Trapezoid

A = \frac{1}{2}(a+b)h

Area of a trapezoid with parallel sides a and b.

Geometry & TrigonometryBasic

Area of a Parallelogram

A = b h

Area of a parallelogram.

Geometry & TrigonometryBasic

Area of an Ellipse

A = \pi a b

Area enclosed by an ellipse.

Geometry & TrigonometryBasic

Volume of a Sphere

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

The volume enclosed by a sphere.

Geometry & TrigonometryBasic

Volume of a Cylinder

V = \pi r^2 h

The volume of a cylinder.

Geometry & TrigonometryBasic

Volume of a Cone

V = \frac{1}{3}\pi r^2 h

The volume of a cone.

Geometry & TrigonometryBasic

Volume of a Cube

V = a^3

The volume of a cube.

Geometry & TrigonometryBasic

Volume of a Box

V = l w h

Volume of a rectangular cuboid.

Geometry & TrigonometryBasic

Volume of a Pyramid

V = \frac{1}{3} B h

Volume of any pyramid.

Geometry & TrigonometryBasic

Surface Area of a Sphere

A = 4\pi r^2

The total surface area of a sphere.

Geometry & TrigonometryBasic

Surface Area of a Cylinder

A = 2\pi r(r + h)

Total surface area of a closed cylinder.

Geometry & TrigonometryIntermediate

Law of Sines

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Relates sides to opposite angles in any triangle.

Geometry & TrigonometryIntermediate

Law of Cosines

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

Generalizes Pythagoras to any triangle.

Geometry & TrigonometryIntermediate

Heron's Formula

A = \sqrt{s(s-a)(s-b)(s-c)}

Area of a triangle from its three sides, s = (a+b+c)/2.

Geometry & TrigonometryIntermediate

Sine Double Angle

\sin(2\theta) = 2\sin\theta\cos\theta

Double-angle identity for sine.

Geometry & TrigonometryIntermediate

Cosine Double Angle

\cos(2\theta) = \cos^2\theta - \sin^2\theta

Double-angle identity for cosine.

Geometry & TrigonometryIntermediate

Pythagorean Identity

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

The fundamental trigonometric identity.

Geometry & TrigonometryIntermediate

Tangent Identity

\tan\theta = \frac{\sin\theta}{\cos\theta}

Defines tangent in terms of sine and cosine.

Geometry & TrigonometryIntermediate

Sine Angle Sum

\sin(A \pm B) = \sin A\cos B \pm \cos A\sin B

Angle addition formula for sine.

Geometry & TrigonometryIntermediate

Cosine Angle Sum

\cos(A \pm B) = \cos A\cos B \mp \sin A\sin B

Angle addition formula for cosine.

Geometry & TrigonometryBasic

Arc Length

s = r\theta

Length of a circular arc (θ in radians).

Geometry & TrigonometryBasic

Area of a Sector

A = \frac{1}{2} r^2 \theta

Area of a circular sector (θ in radians).

Geometry & TrigonometryBasic

Distance Between Two Points

d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

Euclidean distance in the plane.

Geometry & TrigonometryBasic

Midpoint Formula

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

Midpoint of a line segment.

Geometry & TrigonometryBasic

Slope of a Line

m = \frac{y_2 - y_1}{x_2 - x_1}

Steepness of a straight line.

Geometry & TrigonometryBasic

Perimeter of a Square

P = 4a

Total length around a square.

Geometry & TrigonometryBasic

Perimeter of a Rectangle

P = 2(l + w)

Total length around a rectangle.

Geometry & TrigonometryBasic

Perimeter of a Triangle

P = a + b + c

Sum of the three sides of a triangle.

Geometry & TrigonometryBasic

Perimeter of a Parallelogram

P = 2(a + b)

Total length around a parallelogram.

Geometry & TrigonometryBasic

Perimeter of a Rhombus

P = 4a

All four sides of a rhombus are equal.

Geometry & TrigonometryBasic

Perimeter of a Trapezoid

P = a + b + c + d

Sum of all four sides of a trapezoid.

Geometry & TrigonometryBasic

Perimeter of a Regular Polygon

P = n s

Total length around a regular polygon.

Geometry & TrigonometryBasic

Area of a Square

A = a^2

Space enclosed by a square.

Geometry & TrigonometryBasic

Area of a Rhombus

A = \frac{1}{2} d_1 d_2

Area from the two diagonals of a rhombus.

Geometry & TrigonometryBasic

Area of a Kite

A = \frac{1}{2} d_1 d_2

Area from the two diagonals of a kite.

Geometry & TrigonometryIntermediate

Area of a Regular Polygon

A = \frac{1}{2} a P

Area from apothem and perimeter.

Geometry & TrigonometryBasic

Diagonal of a Square

d = a\sqrt{2}

Length of the diagonal of a square.

Geometry & TrigonometryBasic

Diagonal of a Rectangle

d = \sqrt{l^2 + w^2}

Length of the diagonal of a rectangle.

Geometry & TrigonometryIntermediate

Space Diagonal of a Cuboid

d = \sqrt{l^2 + w^2 + h^2}

Longest diagonal through a rectangular box.

Geometry & TrigonometryBasic

Surface Area of a Cube

A = 6a^2

Total surface area of a cube.

Geometry & TrigonometryBasic

Surface Area of a Cuboid

A = 2(lw + lh + wh)

Total surface area of a rectangular box.

Geometry & TrigonometryIntermediate

Surface Area of a Cone

A = \pi r(r + l)

Total surface area of a cone with slant height l.

Geometry & TrigonometryIntermediate

Curved Surface of a Cylinder

A = 2\pi r h

Side (curved) surface area of a cylinder.

Geometry & TrigonometryBasic

Sum of Interior Angles

S = (n - 2)\times 180^\circ

Total of interior angles of an n-sided polygon.

Geometry & TrigonometryIntermediate

Interior Angle (Regular Polygon)

\theta = \frac{(n-2)\times 180^\circ}{n}

Measure of each interior angle of a regular polygon.

Geometry & TrigonometryIntermediate

Cotangent Identity

\cot\theta = \frac{\cos\theta}{\sin\theta}

Cotangent as the ratio of cosine to sine.

Geometry & TrigonometryIntermediate

Reciprocal Trig Identities

\sec\theta = \tfrac{1}{\cos\theta}, \ \csc\theta = \tfrac{1}{\sin\theta}

Secant and cosecant as reciprocals.

Geometry & TrigonometryAdvanced

Tangent Double Angle

\tan(2\theta) = \frac{2\tan\theta}{1 - \tan^2\theta}

Double-angle identity for tangent.

Geometry & TrigonometryIntermediate

Area of Regular Polygon

A = \frac{1}{2} a p

Area from apothem and perimeter.

Geometry & TrigonometryBasic

Interior Angle Sum

S = (n-2)\times 180\degree

Sum of interior angles of an n-sided polygon.

Geometry & TrigonometryIntermediate

Each Interior Angle (Regular)

\theta = \frac{(n-2)\times 180\degree}{n}

Measure of one interior angle of a regular polygon.

Geometry & TrigonometryBasic

Exterior Angle (Regular)

\theta = \frac{360\degree}{n}

Measure of one exterior angle of a regular polygon.

Geometry & TrigonometryIntermediate

Number of Diagonals

D = \frac{n(n-3)}{2}

Count of diagonals in an n-sided polygon.

Geometry & TrigonometryAdvanced

Frustum Volume

V = \frac{1}{3}\pi h(R^2 + Rr + r^2)

Volume of a truncated cone.

Geometry & TrigonometryAdvanced

Torus Volume

V = 2\pi^2 R r^2

Volume of a donut-shaped solid.

Geometry & TrigonometryAdvanced

Spherical Cap Volume

V = \frac{\pi h^2}{3}(3R - h)

Volume of a slice cut from a sphere.

Geometry & TrigonometryAdvanced

Circumradius

R = \frac{abc}{4K}

Radius of a triangle circumscribed circle.

Geometry & TrigonometryAdvanced

Inradius

r = \frac{K}{s}

Radius of a triangle inscribed circle.

Geometry & TrigonometryAdvanced

Tangent Half-Angle

\tan\frac{\theta}{2} = \frac{1-\cos\theta}{\sin\theta}

Expresses the tangent of a half angle.

Geometry & TrigonometryBasic

Cofunction Identity

\sin\theta = \cos(90\degree - \theta)

Sine and cosine of complementary angles are equal.

Geometry & TrigonometryBasic

Secant Definition

\sec\theta = \frac{1}{\cos\theta}

Reciprocal of cosine.

Geometry & TrigonometryBasic

Arc Length (Radians)

s = r\theta

Arc length from radius and central angle in radians.

Geometry & TrigonometryIntermediate

Sector Area (Radians)

A = \frac{1}{2}r^2\theta

Area of a circular sector with angle in radians.

TrigonometryBasic

Sine Ratio (SOH)

\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}

Ratio of the side opposite an angle to the hypotenuse.

TrigonometryBasic

Cosine Ratio (CAH)

\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}

Ratio of the side adjacent to an angle to the hypotenuse.

TrigonometryBasic

Tangent Ratio (TOA)

\tan\theta = \frac{\text{opposite}}{\text{adjacent}}

Ratio of the opposite side to the adjacent side.

TrigonometryIntermediate

Cosecant

\csc\theta = \frac{1}{\sin\theta}

Reciprocal of sine.

TrigonometryIntermediate

Secant

\sec\theta = \frac{1}{\cos\theta}

Reciprocal of cosine.

TrigonometryIntermediate

Cotangent

\cot\theta = \frac{1}{\tan\theta} = \frac{\cos\theta}{\sin\theta}

Reciprocal of tangent.

TrigonometryBasic

Tangent Identity

\tan\theta = \frac{\sin\theta}{\cos\theta}

Tangent equals sine divided by cosine.

TrigonometryBasic

Pythagorean Identity

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

The fundamental trig identity from the unit circle.

TrigonometryIntermediate

Identity: 1 + tan² = sec²

1 + \tan^2\theta = \sec^2\theta

Derived Pythagorean identity dividing by cos².

TrigonometryIntermediate

Identity: 1 + cot² = csc²

1 + \cot^2\theta = \csc^2\theta

Derived Pythagorean identity dividing by sin².

TrigonometryIntermediate

Sine of a Sum

\sin(A+B) = \sin A\cos B + \cos A\sin B

Angle addition formula for sine.

TrigonometryIntermediate

Sine of a Difference

\sin(A-B) = \sin A\cos B - \cos A\sin B

Angle subtraction formula for sine.

TrigonometryIntermediate

Cosine of a Sum

\cos(A+B) = \cos A\cos B - \sin A\sin B

Angle addition formula for cosine.

TrigonometryIntermediate

Cosine of a Difference

\cos(A-B) = \cos A\cos B + \sin A\sin B

Angle subtraction formula for cosine.

TrigonometryAdvanced

Tangent of a Sum

\tan(A+B) = \frac{\tan A + \tan B}{1 - \tan A\tan B}

Angle addition formula for tangent.

TrigonometryAdvanced

Tangent of a Difference

\tan(A-B) = \frac{\tan A - \tan B}{1 + \tan A\tan B}

Angle subtraction formula for tangent.

TrigonometryIntermediate

Double Angle: Sine

\sin 2\theta = 2\sin\theta\cos\theta

Sine of twice an angle.

TrigonometryIntermediate

Double Angle: Cosine

\cos 2\theta = \cos^2\theta - \sin^2\theta

Cosine of twice an angle (also 2cos²θ−1 or 1−2sin²θ).

TrigonometryAdvanced

Double Angle: Tangent

\tan 2\theta = \frac{2\tan\theta}{1 - \tan^2\theta}

Tangent of twice an angle.

TrigonometryAdvanced

Half Angle: Sine

\sin\frac{\theta}{2} = \pm\sqrt{\frac{1-\cos\theta}{2}}

Sine of half an angle.

TrigonometryAdvanced

Half Angle: Cosine

\cos\frac{\theta}{2} = \pm\sqrt{\frac{1+\cos\theta}{2}}

Cosine of half an angle.

TrigonometryAdvanced

Half Angle: Tangent

\tan\frac{\theta}{2} = \frac{1-\cos\theta}{\sin\theta}

Tangent of half an angle.

TrigonometryAdvanced

Product: sin A cos B

\sin A\cos B = \tfrac{1}{2}[\sin(A+B) + \sin(A-B)]

Product-to-sum identity.

TrigonometryAdvanced

Product: cos A cos B

\cos A\cos B = \tfrac{1}{2}[\cos(A-B) + \cos(A+B)]

Product-to-sum identity.

TrigonometryAdvanced

Product: sin A sin B

\sin A\sin B = \tfrac{1}{2}[\cos(A-B) - \cos(A+B)]

Product-to-sum identity.

TrigonometryAdvanced

Sum to Product: sin A + sin B

\sin A + \sin B = 2\sin\tfrac{A+B}{2}\cos\tfrac{A-B}{2}

Sum-to-product identity.

TrigonometryAdvanced

Sum to Product: sin A − sin B

\sin A - \sin B = 2\cos\tfrac{A+B}{2}\sin\tfrac{A-B}{2}

Sum-to-product identity.

TrigonometryAdvanced

Sum to Product: cos A + cos B

\cos A + \cos B = 2\cos\tfrac{A+B}{2}\cos\tfrac{A-B}{2}

Sum-to-product identity.

TrigonometryAdvanced

Sum to Product: cos A − cos B

\cos A - \cos B = -2\sin\tfrac{A+B}{2}\sin\tfrac{A-B}{2}

Sum-to-product identity.

TrigonometryIntermediate

Law of Sines

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Relates sides of any triangle to the sines of opposite angles.

TrigonometryIntermediate

Law of Cosines

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

Generalises Pythagoras to any triangle.

TrigonometryAdvanced

Law of Tangents

\frac{a-b}{a+b} = \frac{\tan\tfrac{A-B}{2}}{\tan\tfrac{A+B}{2}}

Relates two sides and their opposite angles.

TrigonometryIntermediate

Triangle Area (SAS)

\text{Area} = \tfrac{1}{2}ab\sin C

Area from two sides and the included angle.

TrigonometryIntermediate

Heron's Formula

\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}

Triangle area from the three side lengths, where s is the semi-perimeter.

TrigonometryBasic

Degrees to Radians

\text{rad} = \text{deg} \times \frac{\pi}{180}

Convert an angle from degrees to radians.

TrigonometryBasic

Radians to Degrees

\text{deg} = \text{rad} \times \frac{180}{\pi}

Convert an angle from radians to degrees.

TrigonometryAdvanced

Euler's Formula

e^{i\theta} = \cos\theta + i\sin\theta

Links complex exponentials to trigonometry.

TrigonometryAdvanced

De Moivre's Theorem

(\cos\theta + i\sin\theta)^n = \cos n\theta + i\sin n\theta

Powers of complex numbers in trig form.

TrigonometryIntermediate

Sinusoidal Function

y = A\sin(Bx + C) + D

General sine wave with amplitude A, period 2π/B, phase C, shift D.

CalculusIntermediate

Derivative of Sine

\frac{d}{dx}\sin x = \cos x

Derivative of the sine function.

CalculusIntermediate

Derivative of Cosine

\frac{d}{dx}\cos x = -\sin x

Derivative of the cosine function.

CalculusIntermediate

Derivative of Tangent

\frac{d}{dx}\tan x = \sec^2 x

Derivative of the tangent function.

Statistics & ProbabilityBasic

Arithmetic Mean

\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i

The average of a data set.

Statistics & ProbabilityIntermediate

Geometric Mean

GM = \sqrt[n]{x_1 x_2 \cdots x_n}

The nth root of the product of n values.

Probability & CombinatoricsIntermediate

Geometric Probability

P(X=k) = (1-p)^{k-1} p

Probability that the first success occurs on trial k.

Data Science & MLBasic

Classification Accuracy

Accuracy = \frac{TP + TN}{TP + TN + FP + FN}

Fraction of predictions that are correct.

Data Science & MLIntermediate

Precision

Precision = \frac{TP}{TP + FP}

Of all positive predictions, the fraction that were correct.

Data Science & MLIntermediate

Recall (Sensitivity)

Recall = \frac{TP}{TP + FN}

Of all actual positives, the fraction correctly identified.

Data Science & MLIntermediate

F1 Score

F_1 = 2\cdot\frac{Precision \cdot Recall}{Precision + Recall}

Harmonic mean of precision and recall.

Data Science & MLIntermediate

Specificity

Specificity = \frac{TN}{TN + FP}

Of all actual negatives, the fraction correctly identified.

Data Science & MLBasic

Manhattan Distance

d = \sum_{i=1}^{n}|a_i - b_i|

Distance measured along axes at right angles (taxicab geometry).

Optics & WavesBasic

Lens Power

P = \frac{1}{f}

Optical power in dioptres (f in metres).

Fluid MechanicsBasic

Volumetric Flow Rate

Q = Av

Volume of fluid passing per unit time.

ChemistryBasic

Moles from Mass

n = \frac{m}{M}

Number of moles from mass and molar mass.

ChemistryIntermediate

Percent Yield

\% = \frac{\text{actual}}{\text{theoretical}} \times 100

Efficiency of a chemical reaction.

ChemistryBasic

Percent Composition

\% = \frac{\text{mass of element}}{\text{molar mass}} \times 100

Mass percentage of an element in a compound.

Biology & Life SciencesIntermediate

Respiratory Quotient

RQ = \frac{CO_2\ produced}{O_2\ consumed}

Ratio revealing which fuel is being metabolised.

Biology & Life SciencesAdvanced

Hemocytometer Cell Count

C = \bar{n} \times DF \times 10^4

Cells per mL from a counting-chamber average.

Biology & Life SciencesAdvanced

Kleiber's Law

q_0 = 70\,M^{0.75}

Metabolic rate scales with body mass to the ¾ power.

Biology & Life SciencesAdvanced

Respiratory Quotient

RQ = \frac{CO_2\text{ produced}}{O_2\text{ consumed}}

Ratio revealing which fuel is being metabolized.

Health & FitnessIntermediate

BMR (Mifflin, Men)

BMR = 10m + 6.25h - 5a + 5

Basal metabolic rate — daily calories at rest for men.

Health & FitnessIntermediate

BMR (Mifflin, Women)

BMR = 10m + 6.25h - 5a - 161

Basal metabolic rate for women.

Health & FitnessAdvanced

Body Fat % (Navy, Men)

BF = \frac{495}{1.0324 - 0.19077\log_{10}(w-n) + 0.15456\log_{10}h} - 450

US Navy body-fat estimate for men from tape measurements.

Health & FitnessIntermediate

Calories Burned (MET)

C = MET \times m \times t

Energy used during exercise.

Health & FitnessAdvanced

VO₂ Max (Cooper)

VO_2 = \frac{d - 504.9}{44.73}

Aerobic fitness from a 12-minute run distance (metres).

Health & FitnessBasic

Step Length from Height

L \approx 0.415 \times h

Estimated walking step length from height.

Health & FitnessIntermediate

BMR (Katch-McArdle)

BMR = 370 + 21.6\,LBM

Resting calories from lean body mass.

Health & FitnessIntermediate

RMR (Cunningham)

RMR = 500 + 22\,LBM

Resting metabolic rate favoured for athletes.

Health & FitnessIntermediate

MET to Oxygen Uptake

VO_2 = 3.5 \times MET

Oxygen consumption from a MET activity level.

Nutrition & FoodIntermediate

Food Cost Percentage

FC = \frac{c_{ingredients}}{p_{selling}} \times 100

Ingredient cost as a share of menu price — a core restaurant metric.

EngineeringBasic

Volumetric Flow Rate

Q = Av

Volume of fluid passing per unit time.

Materials & CivilAdvanced

Rectangular Area Moment of Inertia

I = \frac{b h^3}{12}

Second moment of area for a rectangular cross-section.

Materials & CivilIntermediate

Hydraulic Radius

R_h = \frac{A}{P}

Cross-sectional flow area divided by wetted perimeter.

Aviation & AeronauticsBasic

Pressure Altitude

PA = (29.92 - QNH)\times 1000 + h

Altitude referenced to standard pressure; correct field elevation for the altimeter setting.

Aviation & AeronauticsAdvanced

Aspect Ratio

AR = \dfrac{b^2}{S}

Ratio of wingspan squared to wing area; higher AR reduces induced drag.

Aviation & AeronauticsAdvanced

Barometric Altitude

h = \dfrac{RT}{g}\ln\dfrac{P_0}{P}

Altitude derived from the ratio of sea-level to measured pressure.

AccountingAdvanced

Double-Declining Balance

D = \dfrac{2}{n}\times Book\ Value

An accelerated depreciation method charging more expense in an asset’s early years.

Business & CommerceAdvanced

Month-over-Month Growth

g = \left(\dfrac{V_1}{V_0}\right) - 1

The percentage change in a metric from one period to the next.

Geography & EarthAdvanced

Barometric Formula

P = P_0 e^{-\frac{Mgh}{RT}}

Atmospheric pressure as a function of altitude.

Geography & EarthAdvanced

Radiometric Dating Age

t = \frac{1}{\lambda}\ln\!\left(1 + \frac{D}{P}\right)

Age of a rock from parent and daughter isotopes.

Unit ConversionsBasic

Kilometers to Miles

\text{mi} = \text{km} \times 0.621371

Convert kilometers to miles.

Unit ConversionsBasic

Miles to Kilometers

\text{km} = \text{mi} \times 1.60934

Convert miles to kilometers.

Unit ConversionsBasic

Meters to Feet

\text{ft} = \text{m} \times 3.28084

Convert meters to feet.

Unit ConversionsBasic

Feet to Meters

\text{m} = \text{ft} \times 0.3048

Convert feet to meters.

Unit ConversionsBasic

Inches to Centimeters

\text{cm} = \text{in} \times 2.54

Convert inches to centimeters.

Unit ConversionsBasic

Nautical Miles to Kilometers

\text{km} = \text{nmi} \times 1.852

Convert nautical miles to kilometers.

Unit ConversionsBasic

Square Meters to Square Feet

\text{ft}^2 = \text{m}^2 \times 10.7639

Convert area from square meters to square feet.

Unit ConversionsBasic

Acres to Square Meters

\text{m}^2 = \text{acre} \times 4046.86

Convert acres to square meters.

Unit ConversionsBasic

Square Km to Square Miles

\text{mi}^2 = \text{km}^2 \times 0.386102

Convert area from square kilometers to square miles.

Unit ConversionsBasic

Cubic Meters to Cubic Feet

\text{ft}^3 = \text{m}^3 \times 35.3147

Convert volume from cubic meters to cubic feet.

Unit ConversionsBasic

Metric Tonnes to Pounds

\text{lb} = \text{t} \times 2204.62

Convert metric tonnes to pounds.

Unit ConversionsBasic

m/s to km/h

\text{km/h} = \text{m/s} \times 3.6

Convert speed from meters per second to km/h.

Unit ConversionsBasic

Kilometers to Miles

\text{mi} = km \times 0.6214

Convert kilometers to miles.

Unit ConversionsBasic

Miles to Kilometers

km = mi \times 1.6093

Convert miles to kilometers.

Unit ConversionsBasic

Inches to Centimeters

cm = in \times 2.54

Convert inches to centimeters.

Unit ConversionsBasic

MPH to KM/H

km/h = mph \times 1.6093

Convert miles per hour to kilometers per hour.

Unit ConversionsBasic

Acres to Square Meters

m^2 = acre \times 4046.9

Convert acres to square meters.

Unit ConversionsBasic

Feet to Meters

m = ft \times 0.3048

Convert feet to meters.

Math Tricks (5)

Urdhva Tiryagbhyam (Vertically & Crosswise)

A general Vedic multiplication method that works for any two numbers. Uses vertical and crosswise multiplication patterns.

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Squaring Numbers Near 50

Quick method to square any number near 50 using the identity (50±d)² = 2500 ± 100d + d².

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Square Any Number (a±b Method)

Use the identity (a+b)(a-b) + b² = a² to square numbers quickly by going to the nearest easy number.

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Duplex Method for Squaring

The Dwandwa (duplex) method squares any number by summing duplex values digit by digit — a general Vedic squaring technique.

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Miles ↔ Kilometres Fast

Multiply miles by 1.6 for km, or divide km by 1.6 for miles. Consecutive Fibonacci numbers are handy approximations.

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