# Open-loop gain

The open-loop gain of an operational amplifier is the gain obtained when no feedback is used in the circuit. Open loop gain is usually exceedingly high; in fact, an ideal operational amplifier has infinite open-loop gain. Typically an op-amp may have an open-loop gain of around $10^5$. Normally, feedback is applied around the op-amp so that the gain of the overall circuit is defined and kept to a figure which is more usable. However the very high gain of the op-amp enables considerable levels of feedback to be applied to achieve required performance. The open-loop gain of an operational amplifier falls very rapidly with increasing frequency. Along with slew rate, this is one of the reasons why operational amplifiers have limited bandwidth.
$A_{\text{OL}}=\frac{V_{\text{out}}}{\left(V^+-V^-\right)}$
As you can see from the definition above, in an ideal amplifier where $V^+=V^-$, the open loop gain ($A_{\text{OL}}$) becomes infinite.