Sodium Correction Calculation Formula

This is the calculation for sodium correction:

Formula One:

[Na]_serumold(Total Body Water)+[Na]_infusion(Volume Given)=[Na]_serumnew(Total Body Water+Voume Given)

Formula Two:

ΔNa=[Na]_serumnew-[Na]_serumold

Rearrange Formula Two:

[Na]_serumnew= ΔNa+[Na]_serumold

Replace Rearranged Formula Two into Formula One:

[Na]_serumold(Total Body Water)+[Na]_infusion(Volume Given)= (ΔNa+[Na]_serumold)(Total Body Water+Voume Given)

Expand:

[Na]_serumold(Total Body Water)+[Na]_infusion(Volume Given)= ΔNa(Total Body Water)+ ΔNa(Volume Given)+[Na]_serumold(Total Body Water)+[Na]_serumold(Volume Given)

Rearrange all with variable (Volume Given) to one side:

[Na]_infusion(Volume Given)-[Na]_serumold(Volume Given)-ΔNa(Volume Given)= ΔNa(Total Body Water)-[Na]_serumold(Total Body Water)+[Na]_serumold(Total Body Water)

Cancelling and grouping variables:

([Na]_infusion-[Na]_serumold-ΔNa)(Volume Given)= ΔNa(Total Body Water)

(Volume given)= ΔNa(Total Body Water)/([Na]_infusion-[Na]_serumold-ΔNa)

In Sarawak Handbook variable ΔNa was rearranged to one side:

ΔNa(Total Body Water)+ΔNa(Volume Given)=[Na]_infusion(Volume Given)-[Na]_serumold(Volume Given)

ΔNa(Total Body Water+Volume Given)=[Na]_infusion(Volume Given)-[Na]_serumold(Volume Given)

ΔNa=[Na]_infusion(Volume Given)-[Na]_serumold(Volume Given)/(Total Body Water+Volume Given)

Volume Given was assumed to be one litre so replacing “Volume Given” with 1 giving:

ΔNa=[Na]_infusion(1)-[Na]_serumold(1)/(Total Body Water+1)

ΔNa=[Na]_infusion-[Na]_serumold/Total Body Water+1