## Area under Curve given Dose and Volume of Distribution Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area Under Curve = Dose/(Volume of Distribution*Elimination Rate Constant)
AUC = D/(Vd*ke)
This formula uses 4 Variables
Variables Used
Area Under Curve - (Measured in Mole Second per Cubic Meter) - Area under Curve (AUC) is the definite integral of a curve that describes the variation of a drug concentration in blood plasma as a function of time.
Dose - (Measured in Mole) - The Dose is the amount of drug administered.
Volume of Distribution - (Measured in Cubic Meter) - The Volume of Distribution is the parameter relating drug concentration in plasma to drug amount in the body.
Elimination Rate Constant - (Measured in 1 Per Second) - Elimination Rate Constant is the rate at which a drug is removed from the body.
STEP 1: Convert Input(s) to Base Unit
Dose: 8 Mole --> 8 Mole No Conversion Required
Volume of Distribution: 9 Liter --> 0.009 Cubic Meter (Check conversion here)
Elimination Rate Constant: 0.058 1 Per Hour --> 1.61111111111111E-05 1 Per Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
AUC = D/(Vd*ke) --> 8/(0.009*1.61111111111111E-05)
Evaluating ... ...
AUC = 55172413.7931035
STEP 3: Convert Result to Output's Unit
55172413.7931035 Mole Second per Cubic Meter -->55172.4137931035 Mole Second per Liter (Check conversion here)
55172.4137931035 Mole Second per Liter <-- Area Under Curve
(Calculation completed in 00.031 seconds)
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K J Somaiya College of science (K J Somaiya), Mumbai
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## < 8 Area under curve Calculators

Area under Curve for Drug Administered Intravenous

## Area under Curve for Drug Administered Intravenous

Formula
"AUC"_{"iv"} = ("AUC"_{"po"}*"D"_{"iv"})/("f"*"D"_{"po"})

Example
"1.894737mol*s/L"=("6mol*s/L"*"12mol")/("9.5"*"4mol")

Calculator
LaTeX
Area under Curve Intravenous = (Area under Curve Non-Intravenous*Dose Intravenous)/(Bioavailability of Drug*Dose Non-Intravenous)
Area under Curve for Drug Administered Orally

## Area under Curve for Drug Administered Orally

Formula
"AUC"_{"po"} = ("f"*"AUC"_{"iv"}*"D"_{"po"})/"D"_{"iv"}

Example
"34.83333mol*s/L"=("9.5"*"11mol*s/L"*"4mol")/"12mol"

Calculator
LaTeX
Area under Curve Non-Intravenous = (Bioavailability of Drug*Area under Curve Intravenous*Dose Non-Intravenous)/Dose Intravenous
Area under Curve of Drug for Dosage Type A

## Area under Curve of Drug for Dosage Type A

Formula
"AUC"_{"dosageA"} = ("F"_{"rel"}*"AUC"_{"dosageB"})*("D"_{"A"}/"D"_{"B"})

Example
"1.19508mol*s/L"=("0.9"*"1.732mol*s/L")*("11.5mol"/"15mol")

Calculator
LaTeX
Area under curve Dosage A = (Relative Bioavailability*Area under curve Dosage B)*(Dose Type A/Dose Type B)
Area under Curve of Drug for Dosage Type B

## Area under Curve of Drug for Dosage Type B

Formula
"AUC"_{"dosageB"} = ("AUC"_{"dosageA"}/"F"_{"rel"})*("D"_{"B"}/"D"_{"A"})

Example
"1.653623mol*s/L"=("1.141mol*s/L"/"0.9")*("15mol"/"11.5mol")

Calculator
LaTeX
Area under curve Dosage B = (Area under curve Dosage A/Relative Bioavailability)*(Dose Type B/Dose Type A)
Area under Curve given Dose and Volume of Distribution

## Area under Curve given Dose and Volume of Distribution

Formula
"AUC" = "D"/("V"_{"d"}*"k"_{"e"})

Example
"55172.41mol*s/L"="8mol"/("9L"*"0.058h⁻¹")

Calculator
LaTeX
Area Under Curve = Dose/(Volume of Distribution*Elimination Rate Constant)
Area under Curve Given Average Plasma Concentration

## Area under Curve Given Average Plasma Concentration

Formula
"AUC" = "C"_{"av"}*"Τ"

Example
"880mol*s/L"="20mol/L"*"44s"

Calculator
LaTeX
Area Under Curve = Average Plasma Concentration*Dosing Interval
Average Plasma Concentration given Area under Curve

## Average Plasma Concentration given Area under Curve

Formula
"C"_{"av"} = "AUC"/"Τ"

Example
"0.03mol/L"="1.320mol*s/L"/"44s"

Calculator
LaTeX
Average Plasma Concentration = Area Under Curve/Dosing Interval
Area under Curve given Volume of Plasma Cleared

## Area under Curve given Volume of Plasma Cleared

Formula
"AUC" = "D"/"CL"

Example
"16.66667mol*s/L"="8mol"/"0.48L/s"

Calculator
LaTeX
Area Under Curve = Dose/Volume of Plasma Cleared

## Area under Curve given Dose and Volume of Distribution Formula

Area Under Curve = Dose/(Volume of Distribution*Elimination Rate Constant)
AUC = D/(Vd*ke)

## What is Pharmacokinetics?

Pharmacokinetics is a branch of pharmacology dedicated to determine the fate of substances administered to a living organism. The substances of interest include any chemical xenobiotic such as: pharmaceutical drugs, pesticides, food additives, cosmetics, etc. It attempts to analyze chemical metabolism and to discover the fate of a chemical from the moment that it is administered up to the point at which it is completely eliminated from the body. Pharmacokinetics is the study of how an organism affects a drug, whereas pharmacodynamics (PD) is the study of how the drug affects the organism. Both together influence dosing, benefit, and adverse effects, as seen in PK/PD models.

## How to Calculate Area under Curve given Dose and Volume of Distribution?

Area under Curve given Dose and Volume of Distribution calculator uses Area Under Curve = Dose/(Volume of Distribution*Elimination Rate Constant) to calculate the Area Under Curve, The Area under Curve given Dose and Volume of Distribution formula is defined as the ratio amount of drug administered to the rate at which a drug is removed from the body with apparent volume in which a drug is distributed. Area Under Curve is denoted by AUC symbol.

How to calculate Area under Curve given Dose and Volume of Distribution using this online calculator? To use this online calculator for Area under Curve given Dose and Volume of Distribution, enter Dose (D), Volume of Distribution (Vd) & Elimination Rate Constant (ke) and hit the calculate button. Here is how the Area under Curve given Dose and Volume of Distribution calculation can be explained with given input values -> 55172.41 = 8/(0.009*1.61111111111111E-05).

### FAQ

What is Area under Curve given Dose and Volume of Distribution?
The Area under Curve given Dose and Volume of Distribution formula is defined as the ratio amount of drug administered to the rate at which a drug is removed from the body with apparent volume in which a drug is distributed and is represented as AUC = D/(Vd*ke) or Area Under Curve = Dose/(Volume of Distribution*Elimination Rate Constant). The Dose is the amount of drug administered, The Volume of Distribution is the parameter relating drug concentration in plasma to drug amount in the body & Elimination Rate Constant is the rate at which a drug is removed from the body.
How to calculate Area under Curve given Dose and Volume of Distribution?
The Area under Curve given Dose and Volume of Distribution formula is defined as the ratio amount of drug administered to the rate at which a drug is removed from the body with apparent volume in which a drug is distributed is calculated using Area Under Curve = Dose/(Volume of Distribution*Elimination Rate Constant). To calculate Area under Curve given Dose and Volume of Distribution, you need Dose (D), Volume of Distribution (Vd) & Elimination Rate Constant (ke). With our tool, you need to enter the respective value for Dose, Volume of Distribution & Elimination Rate Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Area Under Curve?
In this formula, Area Under Curve uses Dose, Volume of Distribution & Elimination Rate Constant. We can use 2 other way(s) to calculate the same, which is/are as follows -
• Area Under Curve = Dose/Volume of Plasma Cleared
• Area Under Curve = Average Plasma Concentration*Dosing Interval
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