# Modulation Index Calculator

URL: https://speedycalculator.com/calculators/physics/modulation/
Last updated: 2026-10-30

> The modulation calculator finds the modulation index of an AM signal from the message and carrier amplitudes, or of an FM signal from the frequency deviation and modulating frequency, with bandwidth and power.

## Inputs

- Modulation type
- Message amplitude A_m
- Carrier amplitude A_c
- Frequency deviation Δf (kHz, Hz, MHz)
- Modulating (message) frequency f_m (kHz, Hz, MHz)

## Results

- Modulation index
- Bandwidth
- Total power vs. carrier (AM)
- Power in sidebands (AM)
- Modulation

## Formula

```
AM: μ = A_m / A_c, B = 2f_m, P_total = P_c(1 + μ²/2) · FM: β = Δf / f_m, B ≈ 2(Δf + f_m) (Carson)
```

## Explanation

Radio stations imprint sound onto a carrier wave by modulating its amplitude (AM) or frequency (FM). The modulation index tells how strongly the carrier is changed: above 1 an AM signal distorts, while FM uses a large index to resist noise.

### How to use the Modulation Index Calculator

- **Modulation type**
- **Message amplitude A_m**
- **Carrier amplitude A_c**
- **Frequency deviation Δf**
- **Modulating (message) frequency f_m**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose AM or FM and enter the values.

### Inputs explained

FieldWhat to enterModulation typeChoose one: Amplitude modulation (AM), Frequency modulation (FM)Message amplitude A_mA numberCarrier amplitude A_cA numberFrequency deviation ΔfUnits: kHz, Hz, MHzModulating (message) frequency f_mUnits: kHz, Hz, MHz

### What each result means

- **Total power vs. carrier (AM)** = (1 + [Modulation index]^2÷2)×100
- **Power in sidebands (AM)** = [Modulation index]^2÷(2 + [Modulation index]^2)×100

### Example values

How the main result changes when **Message amplitude A_m** changes and everything else stays at the example values above:

Message amplitude A_mModulation index0.250.250.3750.3750.50.50.6250.6250.750.7511

## Worked example

Inputs — Modulation type: Amplitude modulation (AM); Message amplitude A_m: 0.5; Carrier amplitude A_c: 1; Modulating (message) frequency f_m: 15 kHz.

Results — **Modulation index = 0.5**; Bandwidth = 30 kHz; Total power vs. carrier (AM) = 112.5 %; Power in sidebands (AM) = 11.111 %; Modulation = Under-modulated.

## Key terms

- **Carrier**: The high-frequency wave that carries the signal.

## FAQ

**What happens if the AM index exceeds 1?**
Over-modulation – the envelope is distorted.

**What is the FM index for broadcast radio?**
Δf = 75 kHz and f_m = 15 kHz give β = 5.

**What is Carson's rule?**
FM bandwidth ≈ 2(Δf + f_m), containing about 98% of the power.

**Why is FM less noisy?**
Noise mostly affects amplitude, which FM receivers ignore.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)