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Op amp gain calculator with output voltage and dB

This op amp gain calculator uses the two basic feedback circuits from the Texas Instruments handbook of operational amplifier applications: inverting gain −Rf/Rin and non-inverting gain 1 + Rf/Rin. Example: Rf = 100 kΩ and Rin = 10 kΩ give a gain of −10 (20 dB); 0.5 V in becomes −5 V out.

Example: Circuit: inverting amplifier · Feedback resistor Rf 100 kΩ · Input resistor Rin (to ground for non-inverting) 10 kΩ · Input voltage (optional) 0.5 V → Gain: G = -10, output -5 V. Source: Texas Instruments, B. Carter & T. R. Brown, Handbook of Operational Amplifier Applications (SBOA092B), Fig. 11–17: inverting E_O = −(R_O/R_I)·E_I, non-inverting E_O = (1 + R_O/R_I)·E_I, voltage follower E_O = E_I; an op amp pushed to saturation behaves unpredictably (read 10.10.2026). Updated: .

kΩ
0 with non-inverting = voltage follower
kΩ
V
0 = off
V
for the saturation check; 0 = off
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Result

Gain
G = -10, output -5 V
Calculation
QuantityValue
Circuitinverting: G = −Rf/Rin
Gain G−100 kΩ / 10 kΩ = -10
Gain in dB = 20 · lg|G|20 · lg 10 = 20 dB
Output voltage-10 × 0.5 V = -5 V
Calculated for an ideal op amp with negative feedback (no input current, no voltage between the inputs). A real op amp only approaches this ideal.

How it is calculated

Inverting: G = −Rf / Rin. Non-inverting: G = 1 + Rf / Rin. The Texas Instruments handbook derives both from two rules for the ideal op amp with negative feedback: no current flows into the inputs, and the voltage between the inputs approaches zero. In the inverting amplifier the input signal drives the inverting input through Rin; in the non-inverting amplifier Rf and Rin form a voltage divider, which is why its gain can never be below 1.

Examples

CircuitRf / RinGaindB
inverting100 kΩ / 10 kΩ−1020 dB
inverting10 kΩ / 10 kΩ−1 (inverter)0 dB
non-inverting90 kΩ / 10 kΩ1020 dB
non-inverting47 kΩ / 10 kΩ5.715.12 dB
non-inverting0 / any1 (voltage follower)0 dB

The gain in dB is a voltage level: NIST SP 811 defines the level of a field quantity as 20 lg(F/F₀) dB, so a gain of 10 is 20 dB and 5.7 is 15.12 dB. The minus sign of the inverting amplifier only means the output is upside down; it does not change the dB value.

Output voltage and saturation

Output = gain × input: −10 × 0.5 V = −5 V. With 2 V in the same circuit would need −20 V, which a ±15 V supply cannot deliver – the op amp saturates. The handbook warns that recovery from saturation is not specified and behaviour then becomes unpredictable, so the calculator flags this case. Rf and Rin as a plain divider are covered by the voltage divider calculator; to combine resistors into a needed Rf, use the parallel resistor calculator.

Frequently asked questions

What is the gain of an inverting op amp?

G = −Rf / Rin. With 100 kΩ and 10 kΩ the gain is −10: the signal is ten times larger and inverted.

What is the gain of a non-inverting op amp?

G = 1 + Rf / Rin. With 90 kΩ and 10 kΩ the gain is 10; with Rf = 0 it is 1, the voltage follower.

How do I convert op amp gain to dB?

dB = 20 · lg|G|. A gain of 10 is 20 dB, a gain of 100 is 40 dB, a gain of 1 is 0 dB.

Why can a non-inverting amplifier not have a gain below 1?

Its gain is 1 plus the resistor ratio, and the ratio is never negative. For less than 1 use an inverting amplifier with Rf smaller than Rin or a voltage divider.

What happens if the output would exceed the supply voltage?

The op amp saturates at its output limit. According to the Texas Instruments handbook its behaviour in saturation is unpredictable – reduce the gain or the input.

Do I have to use kΩ?

Only the ratio counts. Rf and Rin just need the same unit; kΩ is only the preset unit of the fields.

Sources and legal basis

As of: · Editorial policy

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