How to Use the Calculator?
To use the calculator, select whether you are working with an Inverting or Non-Inverting Amplifier. You will see three input boxes: Input Resistance, Feedback Resistance, and Voltage Gain. Simply type your numbers into any two of these boxes, and the calculator will instantly fill in the third box for you. If you need to change your units (like switching from Ohms to kilo-Ohms), just use the dropdown menus; the calculator will neatly convert your numbers on the fly.
What Is an Op-Amp?
An operational amplifier, usually called an op-amp, is an electronic device used to amplify voltage signals. In simple terms, it takes a small input voltage and produces a much larger output voltage.
Op-amps are used in many electronic systems such as audio equipment, sensors, medical devices, radios, and computers. They are extremely popular because with just a few extra components (usually resistors), we can control exactly how much the signal is amplified.
The name operational amplifier comes from early analog computers, where these devices were used to perform mathematical operations like addition, subtraction, integration, and differentiation.
A Typical Op-Amp (Symbol and Terminals)
The symbol of an op-amp is a triangle. It has three main terminals.
On the left side of the triangle there are two inputs. One is marked with a plus sign $+$ and the other with a minus sign $-$. The $+$ terminal is called the non-inverting input, and the $-$ terminal is called the inverting input.
On the right side of the triangle there is a single terminal called the output, usually written as $V_{out}$.
The op-amp amplifies the difference between the two input voltages. If the voltage at the non-inverting input is higher than the voltage at the inverting input, the output becomes positive. If the inverting input voltage is higher, the output becomes negative.
Therefore, the output voltage of an op-amp depends on the difference between its two inputs. If we call the non-inverting input voltage $V_+$ and the inverting input voltage $V_-$, then the relationship can be written as
$$V_{out} = A (V_+ – V_-)$$
Here, $A$ is called the open-loop gain of the op-amp. This value is usually extremely large (often 100,000 or more), which is why feedback circuits are used to control the amplification.
Types of Op-Amp Configurations
There are many ways to connect an op-amp, but two of the most common and important configurations are the inverting amplifier and the non-inverting amplifier. These circuits use resistors to control how much the signal is amplified.
Inverting Op-Amp
In an inverting amplifier, the input signal $V_{in}$ is connected to the inverting terminal through a resistor called $R_{in}$. The non-inverting terminal is connected to ground.
Another resistor called the feedback resistor $R_f$ connects the output back to the inverting input.
Because of the properties of the op-amp, the voltage at the inverting input becomes approximately the same as the non-inverting input. Since the non-inverting input is connected to ground, the inverting input becomes approximately $0\ \text{V}$. This point is called a virtual ground.
The gain of an inverting amplifier is determined by the ratio of the two resistors.
$$A_{inv} = -\frac{R_f}{R_{in}}$$
The negative sign shows that the output signal is inverted. This means if the input voltage increases, the output voltage decreases.
For example, if $R_f = 10,k\Omega$ and $R_{in} = 2,k\Omega$, then the gain becomes
$$A_{inv} = -\frac{10}{2} = -5$$
This means the output voltage is five times larger than the input voltage, but it is flipped upside down.
Non-Inverting Op-Amp
In a non-inverting amplifier, the input signal $V_{in}$ is applied directly to the non-inverting input.
The inverting input is connected to a pair of resistors that form a feedback network. One resistor $R_1$ connects the inverting input to ground, and another resistor $R_2$ connects the inverting input to the output.
In this configuration, the op-amp adjusts its output so that the voltage at the inverting input becomes equal to the voltage at the non-inverting input.
The gain of the non-inverting amplifier is given by
$$A_{non-inv} = 1 + \frac{R_2}{R_1}$$
Notice that this formula does not contain a negative sign, which means the output signal is not inverted. If the input increases, the output increases in the same direction.
For example, if $R_2 = 9,k\Omega$ and $R_1 = 1,k\Omega$, then the gain becomes
$$A_{non-inv} = 1 + \frac{9}{1} = 10$$
This means the output voltage becomes ten times the input voltage, while keeping the same polarity.
Why Feedback Is Important
Both the inverting and non-inverting amplifiers use something called negative feedback. This means part of the output signal is sent back to the input.
Negative feedback helps to control the gain, stabilize the circuit, reduce distortion, and make the amplifier more predictable.
Without feedback, the op-amp’s gain would be so large that even a tiny input difference would drive the output to its maximum limit.
Conclusion
An op-amp is one of the most useful devices in electronics. By simply changing how resistors are connected around it, we can control how signals are amplified.
The inverting amplifier flips the signal and has a gain of
$$A_{inv} = -\frac{R_f}{R_{in}}$$
The non-inverting amplifier keeps the signal in the same direction and has a gain of
$$A_{non-inv} = 1 + \frac{R_2}{R_1}$$
