# How to convert w/w% weight concentration to ppm

In this post, we describe how to convert w/w% (weight concentration of a solution) to ppm (parts per million, or mg/l), with applications to liquid fertilizers.

This method is an approximation for dilute solutions.

We will focus on converting 0.8 w/w% to ppm, with 2ml of fertilizer in a 5 gallon container. This is based on Tropica fertilizer Potassium concentration. We will then verify it with the Rotala Butterfly calculator (answer is 0.845 ppm).

1) 0.8 w/w% = 8g per 1000ml

Here we have made the assumption that 1000ml of solution weighs 1000mg, which is valid for dilute solutions.

2) This is equivalent to: 0.016g per 2ml (in the fertilizer).

3) Now after pouring the fertilizer into the 5 gallon container, the concentration is 16mg per 5 gal = 16mg per 18.9271 liters.

Here we have made the approximation that the amount of fertilizer (2ml) is negligible compared to the volume of the container (5 gal).

4) This is equivalent to 0.845 mg per l or 0.845 ppm as calculated by the Rotala Butterfly calculator!

## Rotala Butterfly Calculator Formula

Let a be the w/w% concentration.

Let b be the amount of fertilizer to use (in ml).

Then,

ppm = (10ab)/18.9271

In the example above,

a=0.8, b=2, so

ppm = (16)/18.9271=0.845 