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Everyday & Health formula solvers

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Basal Metabolic Rate (Harris-Benedict, Men)

BMR=88.362+13.397 m+4.799 h−5.677 a\mathrm{BMR} = 88.362 + 13.397\,m + 4.799\,h - 5.677\,a

Biomedical & ClinicalEveryday & HealthResting energy expenditure for men in kcal per day, by the 1984 Roza and Shizgal revision of the 1919 Harris-Benedict equations.

Basal Metabolic Rate (Harris-Benedict, Women)

BMR=447.593+9.247 m+3.098 h−4.330 a\mathrm{BMR} = 447.593 + 9.247\,m + 3.098\,h - 4.330\,a

Biomedical & ClinicalEveryday & HealthResting energy expenditure for women in kcal per day, by the 1984 Roza and Shizgal revision of the 1919 Harris-Benedict equations.

Basal Metabolic Rate (Mifflin-St Jeor)

BMR=10 m+6.25 h−5 a+s\mathrm{BMR} = 10\,m + 6.25\,h - 5\,a + s

Biomedical & ClinicalEveryday & HealthMifflin and St Jeor's 1990 fit for resting energy expenditure in kcal per day, from mass in kilograms, height in centimetres and age in years.

Blood Alcohol Estimate (Widmark Equation)

BAC=100 Ar m−βt\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.

Body Mass Index (BMI)

BMI=mh2\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.

Body Surface Area (Du Bois Formula)

BSA=0.007184⋅hcm0.725⋅mkg0.425\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.

Body Surface Area (Mosteller Formula)

BSA=hcm⋅mkg3600\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.

Calories Burned from MET, Mass and Time

E=MET⋅m⋅tE = \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.

Dew Point (Magnus Approximation)

Td=c γb−γ,γ=ln⁡ ⁣RH100+b Tc+TT_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).

Fuel Consumption (L/100 km)

C=100 VdC = \frac{100\,V}{d}

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

Heat Index (Rothfusz Regression)

HI=c1+c2T+c3R+c4TR+c5T2+c6R2+c7T2R+c8TR2+c9T2R2\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).

Humidex (Canadian Humidity Index)

H=T+0.5555 (e−10),e=6.11 e5417.753(1273.16−1Td)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.

IV Infusion Rate (mL per Hour)

R=VtR = \frac{V}{t}

Biomedical & ClinicalEveryday & HealthThe rate to set on a volumetric infusion pump: the volume to be infused divided by the time it should take.

Maximum Heart Rate from Age (220 − Age)

HRmax=220−a\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.

Miles per Gallon ↔ L/100 km

C⋅M=235.215C \cdot M = 235.215

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

Recipe Scaling (Ingredient for a New Yield)

Q2=Q1⋅S2S1Q_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.

Target Heart Rate (Karvonen Method)

THR=HRrest+I (HRmax−HRrest)\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.

Unit Price (Price per Unit Quantity)

p=Cmp = \frac{C}{m}

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

Wind Chill (2001 North American Formula)

Twc=13.12+0.6215 T−11.37 V0.16+0.3965 T V0.16T_{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.