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42 results for “distance”

Formulae (41)

Speed = Distance ÷ Time

s = \frac{d}{t}

How fast something moves.

Arithmetic & BasicsBasic

Distance = Speed × Time

d = s \times t

How far something travels.

AlgebraBasic

Absolute Value

|x| = \begin{cases} x & x \ge 0 \\ -x & x < 0 \end{cases}

Distance of a number from zero, always non-negative.

Geometry & TrigonometryBasic

Distance Between Two Points

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

Euclidean distance in the plane.

Data Science & MLBasic

Euclidean Distance

d = \sqrt{\sum_{i=1}^{n}(a_i - b_i)^2}

Straight-line distance between two points in n-dimensional space.

Data Science & MLBasic

Manhattan Distance

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

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

PhysicsBasic

Work Done

W = F d \cos\theta

Work done by a force over a distance.

PhysicsBasic

Speed

v = \frac{d}{t}

Speed equals distance divided by time.

PhysicsAdvanced

Gravitational Potential Energy (General)

U = -\frac{GMm}{r}

Potential energy of two masses at distance r.

PhysicsIntermediate

Projectile Range

R = \frac{v^2\sin 2\theta}{g}

Horizontal distance of a projectile on level ground.

Physics Laws & TheoremsIntermediate

Lens Maker's / Thin Lens

\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

Relates focal length to object and image distances for a thin lens.

Optics & WavesIntermediate

Thin Lens Equation

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Relates focal length to object and image distances.

Biology & Life SciencesAdvanced

Recombination Frequency

RF = \frac{\text{recombinants}}{\text{total offspring}} \times 100

Genetic map distance in centimorgans.

Health & FitnessAdvanced

VO₂ Max (Cooper)

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

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

Health & FitnessBasic

Running Pace

\text{pace} = \frac{t}{d}

Time taken to cover one unit of distance.

Astronomy & SpaceAdvanced

Hubble's Law

v = H_0 d

Recession velocity of galaxies with distance.

Astronomy & SpaceAdvanced

Parallax Distance

d = \frac{1}{p}

Distance in parsecs from parallax angle in arcseconds.

Astronomy & SpaceAdvanced

Apparent Brightness

b = \frac{L}{4\pi d^2}

Observed brightness from luminosity and distance.

Astronomy & SpaceAdvanced

Distance Modulus

m - M = 5\log_{10}(d) - 5

Relates apparent and absolute magnitude to distance.

Astronomy & SpaceBasic

Light-Year

d = c \times t

Distance light travels in a given time.

Aviation & AeronauticsBasic

Flight Time

t = \dfrac{d}{GS}

Time en route equals distance divided by ground speed.

Aviation & AeronauticsIntermediate

Glide Ratio

GR = \dfrac{d}{h} = \dfrac{L}{D}

Horizontal distance traveled per unit of altitude lost equals the lift-to-drag ratio.

Aviation & AeronauticsIntermediate

Specific Range

SR = \dfrac{GS}{\dot{f}}

Distance flown per unit of fuel; maximizing it gives best fuel economy.

Aviation & AeronauticsIntermediate

Point of No Return

PNR = \dfrac{E \cdot GS_{out} \cdot GS_{back}}{GS_{out}+GS_{back}}

Farthest distance an aircraft can fly and still return with available endurance.

Aviation & AeronauticsAdvanced

Takeoff Ground Roll

s = \dfrac{V_{LO}^2}{2a}

Approximate ground-roll distance assuming constant acceleration to lift-off speed.

Aviation & AeronauticsAdvanced

Great Circle Distance

d = R\arccos(\sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos\Delta\lambda)

Shortest distance between two points on the Earth for long-range navigation.

Aviation & AeronauticsIntermediate

Glide Ratio

GR = \frac{\text{horizontal distance}}{\text{altitude lost}}

Distance traveled forward per unit of height lost.

Everyday MathBasic

Fuel Economy (mpg)

\text{mpg} = \frac{\text{Miles}}{\text{Gallons}}

Distance traveled per gallon of fuel.

Everyday MathBasic

Average Speed

v = \frac{d}{t}

Distance covered per unit time.

Everyday MathBasic

Travel Time

t = \frac{d}{v}

Time needed to cover a distance at a given speed.

Geography & EarthAdvanced

Haversine Distance

d = 2r\arcsin\sqrt{\sin^2\frac{\Delta\phi}{2} + \cos\phi_1\cos\phi_2\sin^2\frac{\Delta\lambda}{2}}

Great-circle distance between two lat/long points.

Geography & EarthBasic

Map Scale

\text{Scale} = \frac{\text{map distance}}{\text{ground distance}}

Ratio of map distance to real-world distance.

Geography & EarthAdvanced

Earth Curvature Drop

h \approx \frac{d^2}{2R}

Approximate drop of the horizon over distance d.

Geography & EarthBasic

Degrees to Distance

1^\circ \text{lat} \approx 111\ \text{km}

Approximate ground distance per degree of latitude.

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.

Computer ScienceAdvanced

Hamming Distance

d(x,y) = \sum_i [x_i \ne y_i]

Number of positions at which two strings differ.

Math Tricks (1)

Miles ↔ Kilometres Fast

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

View trick