Calculate CMRR, differential gain, or common mode gain from any two values, with V/V, ratio, and dB unit options for amplifier analysis.
CMRR Formula
CMRR, or common mode rejection ratio, compares an amplifier’s differential gain to its common mode gain. The calculator uses the ratio form as the base calculation, then converts to or from decibels when you select dB.
CMRR = A_d / A_cm
A_d = A_cm * CMRR
A_cm = A_d / CMRR
CMRR_dB = 20 * log10(CMRR)
CMRR = 10^(CMRR_dB / 20)
- CMRR = common mode rejection ratio, expressed as a plain ratio
- CMRR_dB = common mode rejection ratio in decibels
- A_d = differential gain, usually in V/V or dB
- A_cm = common mode gain, usually in V/V or dB
- log10 = base-10 logarithm
If you enter differential gain and common mode gain, the calculator finds CMRR. If you enter common mode gain and CMRR, it finds differential gain. If you enter differential gain and CMRR, it finds common mode gain. For dB inputs, the calculator converts the value to a voltage ratio first, performs the calculation, then converts the result back to the selected output unit.
Common CMRR Ranges
Higher CMRR means better rejection of signals that appear equally on both inputs, such as electrical noise or interference.
| CMRR Ratio | CMRR dB | General Interpretation |
|---|---|---|
| 100:1 | 40 dB | Low rejection for precision measurements |
| 1,000:1 | 60 dB | Moderate common mode rejection |
| 10,000:1 | 80 dB | Good rejection for many amplifier circuits |
| 100,000:1 | 100 dB | High rejection, common in precision instrumentation amplifiers |
| 1,000,000:1 | 120 dB | Very high rejection for demanding measurement circuits |
CMRR Examples
Example 1: Calculate CMRR from two gains
You have a differential gain of 10,000 V/V and a common mode gain of 1 V/V.
CMRR = A_d / A_cm
CMRR = 10000 / 1 = 10000
CMRR_dB = 20 * log10(10000) = 80 dB
The CMRR is 10,000:1, or 80 dB.
Example 2: Calculate common mode gain
You have a differential gain of 2,000 V/V and a CMRR of 100 dB.
CMRR = 10^(100 / 20) = 100000
A_cm = A_d / CMRR
A_cm = 2000 / 100000 = 0.02 V/V
The common mode gain is 0.02 V/V.
CMRR FAQ
What does a higher CMRR mean?
A higher CMRR means the amplifier rejects more common mode signal compared with the differential signal it is meant to amplify. In practical terms, higher CMRR helps reduce noise that appears on both inputs at the same time.
Why does the dB formula use 20 instead of 10?
CMRR is based on voltage gain ratios, so the decibel conversion uses 20 * log10(ratio). The factor 10 is used for power ratios, not voltage or amplitude ratios.
Can CMRR be calculated if common mode gain is zero?
No. The ratio formula divides by common mode gain. If common mode gain is zero, the mathematical result would be undefined or idealized as infinite rejection. For a real calculation, use a measured nonzero common mode gain.
