There are a lot of formulas a medical student need to memorise, and one of them is this.
Note that, i really believe that getting an ionized calcium is easier and more accurate, but nevertheless this formula is always asked as a pimped question.
So what does the formula say?
For every g/dL of albumin below its average value (which is 4 g/dL), the calcium will decrease by 0.8 mg/dL due to its binding to the albumin.So…
Corrected calcium (mg/dL) = Measured calcium (mg/dL) + 0.8 (4 – albumin in g/dL)
- Note the units used: g/dL for albumin and mg/dL for calcium, which are not SI unit.
- In my country, SI unit is used as standard.
therefore, to memorise this is very difficult for me. You can do it in two ways:
- Convert the calcium and albumin to mg/dL and g/dL respectively, use the formula and convert back the value of calcium to mmol/L later.
- Or you could choose to understand….
Why does in SI unit, the formula is somehow like this?
Corrected calcium (mmol/L) = Measured calcium (mmol/L) + 0.02 (40 – albumin in g/L)
- I’ve always wondered, how do we get this formula in mmol/L from the initial mg/dL formula?
- It involves a little bit mathematics.
Before getting started, need to understand there are 2 parts of the formula: measured & “lost” calcium
Corrected Ca2+ = p mg/dL
Measured Ca2+ = q mg/dL
Albumin = r g/dL
Using the mg/dL formula,
p mg/dL = q mg/dL + [0.8 (4 g/dL – r g/dL)] mg/dL
1 mg/dL of Ca2+ = 1/4 mmol/L of Ca2+
p/4 mmol/L = q/4 mmol/L + 0.2 (4 g/dL – r g/dL)
Substitute p/4 = x and q/4 = y, and so the formula becomes
- x mmol/L = y mmol/L + 0.2 (4 g/dL – r g/dL) mmol/L = y mmol/L + (0.8 – 0.2r) mmol/L
Now, the next step is confusing. But need to understand that:
- What is important is you need to get back the products of multiplication of 2nd part of the formula, which is
(0.8 – 0.2r) mmol/L.
- Because 1 g/dL of albumin = 10 g/L, it would become (40 – 10r) mmol/L.
Using simple mathematics,
0.8 – 0.2r = z (40 – 10r)
Let’s assume r = 1,
0.8 – 0.2 = z (40 – 10)
0.6/30 = z
z = 0.02
So in the end, you will get the formula
Corrected Calcium (mmol/L) = Measured Calcium (mmol/L) + 0.02 (40 – albumin in g/L)
To prove that this is right, let’s work it in opposite way (mmol/L -> mg/dL)
– To convert it, the whole formula is multiplied by 4
= 4y + 0.08 (40 – albumin in g/L)
= 4y + 0.08 (40 – z)
Since 40 g/L = 4 g/L,
0.08 (40 – z) = a (4 – z/10)
Assume z = 10,
0.08 (30) = a (4-1)
a = [0.08 (30)]/3 = 0.08 (10) = 0.8
In the end, you would get back the equation
Corrected calcium in mg/dL = measured calcium in mg/dL + 0.8 (4 – albumin in g/dL)