Relationship between normality and molarity
The normality of a solution is the molarity of the solution multiplied by the number of equivalents per mole:

$$\mathrm{N} = \mathrm{{eq\over mol}}\cdot\mathrm{M}= \mathrm{{eq\over mol}}\cdot\mathrm{{mol\over L}}=\mathrm{{eq\over L}}$$

Example: Calculate the normality of a 1 $\mathrm{M}$ solution of $\ce{H2SO4}$. There are 2 equivalents per mole, from the reaction

$$\ce{H2SO4 -&gt; 2H+ + SO4^{2-}}$$

which yields 2 moles of $\ce{H+}$ for every 1 mole of $\ce{H2SO4}$.

Using the relation given above, we find that a 1 $\mathrm{M}$ solution of $\ce{H2SO4}$ is 2 $\mathrm{N}$:

$$\mathrm{{2\;eq\over mol}}\cdot\mathrm{1\;M}=2\;\mathrm{N}$$

One resource you might find useful in order to check your math is Sigma-Aldrich's Normality &amp; Molarity Calculator. Additionally, there are details relevant to the definitions of molarity and normality that you might find clearer that the ones you've conveyed in your question.