Other Common Formulas
Circle: Circumference = pi x D. pi: the ratio of the circumference of a circle to its diameter. Pi is always the same number, no matter which circle you use to compute it. For the sake of usefulness people often need to approximate pi. For many purposes you can use 3.14159 = 3.1416, which is really pretty good, but if you want a better approximation you can use a computer to get it. Here’s pi to many more digits: 3.14159265358979323846.
AREA
Triangle: A = (ab)/2 , in which a is the base and b the height.
Square: A = a2, in which a is one of the sides.
Rectangle: A = ab, in which a is the base and b the height.
Trapezoid: A = (h(a + b))/2, in which h is the height, a the longer parallel side, and b the shorter.
Regular pentagon: A = 1.720a2, in which a is one of the sides.
Regular hexagon: A = 2.598a2, in which a is one of the sides.
Regular octagon: A = 4.828a2, in which a is one of the sides.
Circle: A = pi times the square of the length of the radius, or “pi r squared”
Area: Unit Abbr SI/metric Imperial
Acre = A = 4,047 m2 = 43,560 ft2.
Are = a = 100 m2 = 1076.39 ft2.
Hectare = ha = 10,000 m2 = 2.471 A.
Square centimeter = cm2 = 100 mm2 =.155 in2.
Square foot = ft2 =.0929 m2 = 144 in2.
Square inch = in2 = 6.4516 cm2..
Square kilometer = km2 = 1,000,000 m2 =.386 mi2.
Square meter = m2 = 10,000 cm2 = 10.764 ft2.
Square mile = mi2 = 2.59 km2 = 640 A.
Square millimeter = mm2 = .00155 in2.
Square rod = rd2 = 25.293 m2 = 272.25 ft2.
Square yard = yd2 =.836 m2 = 9 ft2.
VOLUME
Cube: V = a3, in which a is one of the edges.
Rectangular prism: V = abc, in which a is the length, b is the width, and c the depth.
Pyramid: V = (Ah)/3, in which A is the area of the base and h the height.
Cylinder: V = pi r2h, in which pi is 3.1416, r the radius of the base, and h the height.
Cone: V = (pi r2h)/3, in which pi is 3.1416, r theradius of the base, and h the height.
Sphere: V = (4 pi r3)/3, in which pi is 3.1416 and r the radius.
Basic Geometry:
Rectangle: Area (A) = Width (w) x Height (h).
Triangle: Area (A) = ¹D2 Base (b) x Height (h).
Pythagorean Theorem: If a right triangle has hypotenuse (c) and sides (a) and (b), then: c2 = a2 + b2.
Trapezoid: Area (A) = [(a+b) x h] / 2.
Circle: Area (A) = (pi)r squared. Circumference (C) = 2(pi)r. pi = 3.1416 r= radius
Cone: Volume (V) = [(pi)r squared * h]/3.
Area of curved surface: A = (pi)r * square root of r squared +h squared.
Sphere: Volume (V) = [4(pi) r cubed] / 3. Surface Area = A = 4(pi)r squared.
Right Cylinder (can): Volume (V) = (pi) * r squared * h. Lateral surface area (A) = 2*(pi) * r * h.
MISCELLANEOUS
Distance in feet traveled by falling body: d = 16t2, in which t is the time in seconds.
Speed of sound in feet per second through any given temperature of air: take the square root of (273 + t), in which t is the temperature Centigrade, multiply it by 1087, and divide the result by 16.52.
Cost in cents of operation of electrical device: C = (Wtc)/1000, in which W is the number of watts,t the time in hours, and c the cost in cents per kilowatt-hour.
Conversion of matter into energy (Einstein’s Theorem): E = mc2, in which E is the energy in ergs, m the mass of the matter in grams, and c the speed of light in centimeters per second: (c2 = 9 x 1020)
Roman to Ariabic Numbers:
I: The easiest way to note down a number is to make that many marks – little I’s. Thus I means 1, II means 2, III means 3. However, four strokes seemed like too many….
I = 1
II = 2
III = 3
IV = 4
V: So the Romans moved on to the symbol for 5 – V. Placing I in front of the V — or placing any smaller number in front of any larger number — indicates subtraction. So IV means 4. After V comes a series of additions – VI means 6, VII means 7, VIII means 8.
V = 5
VI = 6
VII = 7
VIII = 8
X: X means 10. But what about 9? Same thing. IX means to subtract I from X, leaving 9. Numbers in the teens, twenties and thirties follow the same form as the first set, only with X’s indicating the number of tens. So XXXI is 31, and XXIV is 24.
IX = 9
X = 10
XX = 20
XXX = 30
XL = 40
L: L means 50. Based on what you’ve learned, I bet you can figure out what 40 is. If you guessed XL, you’re right = 10 subtracted from 50. And thus 60, 70, and 80 are LX, LXX and LXXX.
L = 50
LX = 60
LXX = 70
LXXX = 80
XC = 90
C: C stands for centum, the Latin word for 100. A centurion led 100 men. We still use this in words like “century” and “cent.” The subtraction rule means 90 is written as XC. Like the X’s and L’s, the C’s are tacked on to the beginning of numbers to indicate how many hundreds there are: CCCLXIX is 369.
C = 100
CC = 200
CCC = 300
CCCC = 400
D: D stands for 500. As you can probably guess by this time, CD means 400. So CDXLVIII is 448. (See why we switched systems?)
D = 500
DC = 600
DCC = 700
DCCC = 800
V: Larger numbers were indicated by putting a horizontal line over them, which meant to multiply the number by 1,000. Hence the V at left has a line over the top, which means 5,000. This usage is no longer current, because the largest numbers usually expressed in the Roman system are dates, as discussed above.
CM = 900
M: is 1,000. You see a lot of Ms because Roman numerals are used a lot to indicate dates. For instance, this page was written in the year of Nova Roma’s founding, 1998 CE (Common Era; Christians use AD for Anno Domini, “year of our Lord”). That year is written as MCMXCVIII.
M = 1000
MM = 2000
MMM = 3000
MMMM = 4000
V = 5000
VM = 6000
VMM = 7000
VMMM = 8000
MX = 9000
X = 10000
XX = 20000
XXX = 30000
XXXX = 40000
L = 50000
LX = 60000
LXX = 70000
LXXX = 80000
XC = 90000
C = 100000
CC = 200000
CCC = 300000
CCCC = 400000
D = 500000
DC = 600000
DCC = 700000
DCCC = 800000
CM = 900000
M = 1000000.
Commonly Used Drug Therapeutic Range (Levels):
Therapeutic drug monitoring (TDM) has several major clinical applications: To monitor compliance. To increase efficacy. To increase safety (guard against toxicity as narrow therapeutic index). To protect against medicolegal actions. Individual variation in drug absorption, distribution, metabolism, and excretion. Alterations in predicted drug concentrations because of disease. Alterations in predicted drug concentrations because of interactions with other medications.
Drug level = Dosing rate/Clearance.
Timing: Blood samples for TDM should be obtained in the elimination phase of drug dosing, because these levels are more reliable than those drawn during the absorption or distribution phases. Determining the elimination phase requires knowing when the peak concentration (Cmax) occurs, as well as the rapid fall off due to redistribution. Errors in the timing of samples (before steady-state has been reached or too early in a dosing interval) can produce misleading results and inappropriate dosing decisions.
Acetaminophen–> 10-20 mg/L, toxic @ >150 mg/L 5 hr after ingestion.
Alcohol–> 0, toxic @ 150-300 mg/dl: confusion, 300-450: stupor, >400: coma/ death.
Amikacin –> Peak 25-30, trough <10 mcg/mL.
Amiodarone –> 1-3.0 mcg/mL.
Amitriptyline –> 100-250 ng/mL.
Amobarbital –> 7-15 mcg/ml.
Bromide–> 20-120 mg/dl, toxic @ >150 mg/dl.
Carbamazepine –> 4-12 mcg/mL. = Trough Level optimal timing is just prior to next dose.
Chloramphenicol –> Peaks 10-15, trough <5 mcg/mL.
Clonazepam –> 0.02-0.10 mcg/ml.
Cyclosporine –> 100-300 ng/ml (50-150 renal transplant, 150-250 heart or liver).
Desipramine –> 150-300 ng/mL.
Digoxin –> 0.8-2.0 ng/mL. Optimal timing is just prior to next dose.
Digitoxin–> 5-40 ng/ml.
Diphenylhydantoin–> 10-20 mcg/ml.
Disopyramide –> 2-5 mcg/mL.
Doxepin –> 75-200 ng/mL.
Ethosuximide–> 40-100 mcg/ml. = Trough Level optimal timing is just prior to next dose.
Flecainide –> 0.2-1.0 mcg/mL.
Gentamicin –> Peaks 6-8.0, trough <2.0 mcg/mL.
Glutethimide–> 1-7 mcg/ml.
Imipramine –> 150-300 ng/mL.
Lidocaine –> 2-5 mcg/mL.
Lithium –> 0.5-1.4 mEq/L, toxic @ 2.0 mEq/L. = Li trough Level, optimal timing is just prior to first morning dose.
Meprobamate–> 10-20 mcg/ml, toxic @ 30-70 mcg/ml: coma.
Mexiletine –> 1-2 mcg/ml.
Nortriptyline –> 50-150 ng/mL.
Pentobarbital–> 4-6 mcg/ml.
Phenobarbital –> 10-40 mEq/mL (mcg/ml), toxic @ >40 mcg/ml. = Trough Level optimal timing is just prior to next dose.
Phenytoin –> 8-20 mcg/mL, 4-10 if azotemia or decr alb.
Primidone–> 4-12 mcg/ml.
Prograf –> 5-10 ng/ml.
Procainamide –> 4-8.0 mcg/mL. NAPA Level @ 10-30 mcg/ml, optimal timing is just prior to next procainamide dose.
Propranolol–> 50-100 ng/ml.
Quinidine –> 2.5-5.0 mcg/mL, toxic @ >8 mcg/ml.
Salicylate –> 15-25 mg/dL, toxic @ 300 mg/L.
Secobarbital–> 3-5 mcg/ml.
Streptomycin –> Peak 10-20, trough <5 mcg/ml.
Theophylline –> 5-20 mcg/mL. Optimal timing is 8-12 hrs after once daily dose.
Tocainide –> 4-10 mcg/ml.
Valproic acid –> 50-100 mcg/mL. Therapeutic Levels for mania @ 45-125 mcg/ml, optimal timing is just prior to next procainamide dose. For epilepsy @ 50-100 mcg/ml, optimal timing is just prior to next procainamide dose.
Vancomycin –> Peaks 30-40, trough <10 mcg/mL. Vanc Trough: 5–15 mg/L T-1/2 = 6hr; If uremia or renal dysfunction, keep peak level < 30–40 mg/L to avoid toxicity (deafness).
***All levels may vary depending on the reference lab.
