Formula solver index — formula.expert

Body Mass Index (BMI)

\mathrm{BMI} = \frac{m}{h^2}

Everyday & HealthBody mass index: mass divided by the square of height, the population screening ratio defined by Quetelet in 1832.

Maximum Heart Rate from Age (220 − Age)

\mathrm{HR}_{max} = 220 - a

Everyday & HealthThe 220-minus-age estimate of maximum heart rate in beats per minute, the rule of thumb printed on every gym treadmill.

Target Heart Rate (Karvonen Method)

\mathrm{THR} = \mathrm{HR}_{rest} + I\,(\mathrm{HR}_{max} - \mathrm{HR}_{rest})

Everyday & HealthTraining heart rate at a chosen fraction of heart rate reserve, the range between resting and maximum rate.

Body Surface Area (Mosteller Formula)

\mathrm{BSA} = \sqrt{\frac{h_{cm} \cdot m_{kg}}{3600}}

Everyday & HealthBody surface area in square metres by Mosteller's 1987 square-root simplification of the older exponential fits.

Body Surface Area (Du Bois Formula)

\mathrm{BSA} = 0.007184 \cdot h_{cm}^{0.725} \cdot m_{kg}^{0.425}

Everyday & HealthBody surface area by the 1916 Du Bois power fit, still the reference against which newer formulas are compared.

Calories Burned from MET, Mass and Time

E = \mathrm{MET} \cdot m \cdot t

Everyday & HealthEnergy expended during an activity: one MET is defined as one kilocalorie per kilogram of body mass per hour.

Blood Alcohol Estimate (Widmark Equation)

\mathrm{BAC} = \frac{100\,A}{r\,m} - \beta t

Everyday & HealthChemistryWidmark's 1932 estimate of blood alcohol concentration from alcohol consumed, body mass, a distribution ratio and elapsed time. An estimate only, never a fitness-to-drive test.

Wind Chill (2001 North American Formula)

T_{wc} = 13.12 + 0.6215\,T - 11.37\,V^{0.16} + 0.3965\,T\,V^{0.16}

Everyday & HealthThermodynamicsThe wind chill index adopted by Canada and the United States in 2001, from air temperature and wind speed at 10 m.

Dew Point (Magnus Approximation)

T_d = \frac{c\,\gamma}{b - \gamma}, \quad \gamma = \ln\!\frac{\mathrm{RH}}{100} + \frac{b\,T}{c + T}

Everyday & HealthThermodynamicsDew point from air temperature and relative humidity by the Magnus formula with the WMO's Sonntag coefficients (b = 17.62, c = 243.12 °C).

Humidex (Canadian Humidity Index)

H = T + 0.5555\,(e - 10), \quad e = 6.11\,e^{5417.753\left(\frac{1}{273.16} - \frac{1}{T_d}\right)}

Everyday & HealthThermodynamicsEnvironment Canada's humidex: air temperature raised by the excess vapour pressure computed from the dew point.

Heat Index (Rothfusz Regression)

\mathrm{HI} = c_1 + c_2 T + c_3 R + c_4 T R + c_5 T^2 + c_6 R^2 + c_7 T^2 R + c_8 T R^2 + c_9 T^2 R^2

Everyday & HealthThermodynamicsThe US National Weather Service heat index, Rothfusz's nine-term regression through Steadman's apparent-temperature table (T in °F, R in percent).

Fuel Consumption (L/100 km)

C = \frac{100\,V}{d}

Everyday & HealthFuel consumption in litres per hundred kilometres from the fuel burned and the distance covered.

Miles per Gallon ↔ L/100 km

C \cdot M = 235.215

Everyday & HealthThe reciprocal relation between litres per hundred kilometres and US miles per gallon: their product is always 235.215.

Unit Price (Price per Unit Quantity)

p = \frac{C}{m}

Everyday & HealthPrice per unit of quantity, the number that makes two package sizes comparable on a shelf.

Recipe Scaling (Ingredient for a New Yield)

Q_2 = Q_1 \cdot \frac{S_2}{S_1}

Everyday & HealthIngredient quantity rescaled from the yield a recipe was written for to the yield you actually want.