Inverting Amplifier
Vout = −Vin × Rf/Ri
Quick answer
This calculator solves Vout = −Vin × Rf / Ri for Output Voltage. With Input Voltage 26.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ, the result is -12 V. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The inverting amplifier feeds the input signal through Ri to the inverting terminal of the op-amp, while the non-inverting input is grounded. The output is inverted (180 degrees out of phase) with a gain magnitude set by the Rf/Ri ratio. The input impedance equals Ri because the inverting input is at virtual ground. This configuration is preferred for summing amplifiers, integrators, and differentiators. The gain can be less than, equal to, or greater than unity depending on the resistor ratio.
Variables
- Vout — Output voltage (V)
- Vin — Input voltage (V)
- Rf — Feedback resistor (Ω)
- Ri — Input resistor (Ω)
Practical Notes
The inverting input is a virtual ground, meaning it sits at approximately 0V during operation. Input impedance is set by Ri, which is lower than the non-inverting configuration. For best DC accuracy, place a resistor equal to Rf||Ri on the non-inverting input to cancel bias current offset.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Vout | Output Voltage | V | pV, nV, µV, mV, V, kV |
| Vin | Input Voltage | V | pV, nV, µV, mV, V, kV |
| Rf | Feedback Resistor | kΩ | mΩ, Ω, kΩ, MΩ |
| Ri | Input Resistor | kΩ | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Input Voltage 26.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ
- 2. The relation: Vout = −Vin × Rf / Ri
- 3. Substitute: Vin = 26.4 V, Rf = 10 kΩ, Ri = 22 kΩ
- 4. Result: Output Voltage = -12 V
Related quantities from the same inputs
- P = V² / R = 69.7 mW
- I = V / R = 2.64 mA
Worked examples
Minimum range
Given: Input Voltage 0.726 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ
Result: Output Voltage = -0.33 V
Low range
Given: Input Voltage 7.26 V, Feedback Resistor 1 kΩ, Input Resistor 2.2 kΩ
Result: Output Voltage = -3.3 V
Typical
Given: Input Voltage 26.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ
Result: Output Voltage = -12 V
High range
Given: Input Voltage 0.506 kV, Feedback Resistor 100 kΩ, Input Resistor 0.22 MΩ
Result: Output Voltage = -0.23 kV
Maximum range
Given: Input Voltage 5.06 kV, Feedback Resistor 1 MΩ, Input Resistor 2.2 MΩ
Result: Output Voltage = -2.3 kV
Solving for each variable
Solve for Output Voltage
Input Voltage 0.726 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ → -0.33 V
Solve for Input Voltage
Output Voltage 0.33 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ → -0.726 V
Solve for Feedback Resistor
Output Voltage 0.33 V, Input Voltage 0.726 V, Input Resistor 0.22 kΩ → -100 Ω
Solve for Input Resistor
Output Voltage 0.33 V, Input Voltage 0.726 V, Feedback Resistor 100 Ω → -0.22 kΩ
How Output Voltage changes with Input Voltage
| Input Voltage (input) | Output Voltage (result) |
|---|---|
| 5.81 V | -2.641 V |
| 14.53 V | -6.602 V |
| 29.05 V | -13.2 V |
| 43.58 V | -19.81 V |
| 58.1 V | -26.41 V |
| 87.15 V | -39.61 V |
| 116.2 V | -52.82 V |
| 0.2324 kV | -105.6 V |
| 0.4067 kV | -0.1849 kV |
| 0.581 kV | -0.2641 kV |
The same result in other units
| Unit | Value |
|---|---|
| mV | -12000 |
| V | -12 |
| kV | -0.012 |
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<p><a href="https://vbatpower.com/formulas/opamp-invert/">Inverting Amplifier</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Inverting Amplifier?
Use Vout = −Vin × Rf / Ri. With Input Voltage 26.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ, Output Voltage works out to -12 V.
What is the formula for Inverting Amplifier?
The formula is Vout = −Vin × Rf / Ri. The inverting amplifier feeds the input signal through Ri to the inverting terminal of the op-amp, while the non-inverting input is grounded.
How do you find Input Voltage when you know the other values?
Rearrange for Input Voltage: with Output Voltage 0.33 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ, Input Voltage is -0.726 V.
How do you find Feedback Resistor when you know the other values?
Rearrange for Feedback Resistor: with Output Voltage 0.33 V, Input Voltage 0.726 V, Input Resistor 0.22 kΩ, Feedback Resistor is -100 Ω.
What units does Inverting Amplifier use?
Output Voltage is shown in mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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