Modulation Calculator — AM & FM Modulation Index, Bandwidth, Power
Calculate the modulation index, bandwidth, sideband frequencies, and (for AM) power efficiency for amplitude or frequency modulation. Enter carrier frequency, message frequency, and the appropriate amplitude or frequency-deviation values.
Modulation type
MHz
kHz
V
V
m = Am / Ac — must be ≤ 1 for standard AM; 100% modulation at m = 1
- 1
Carrier amplitude Ac
10 - 2
Message amplitude Am
7 - 3
Modulation index m = Am ÷ Ac
7 ÷ 10 = 0.700m ≤ 1 for undistorted AM; m = 1 is 100 % modulation.
How does this calculator work?
AM modulation index m = Am/Ac; bandwidth = 2·fm; total power = Pc·(1+m²/2); efficiency = m²/(2+m²). FM modulation index β = Δf/fm; Carson bandwidth = 2·(Δf+fm). Keep m ≤ 1 for distortion-free AM. FM broadcast uses Δf=75 kHz, giving BW≈180 kHz per channel.
Formula
How this is calculated
Modulation is the process of encoding information onto a carrier wave by varying one of its properties. In Amplitude Modulation (AM), the carrier's amplitude is varied proportionally to the message signal. The modulation index m = Am/Ac measures the depth of modulation: at m = 0 there is no modulation (pure carrier), at m = 1 (100% modulation) the amplitude swings fully between 0 and 2Ac, and m > 1 causes overmodulation with distortion. The transmitted spectrum consists of the carrier at fc, an upper sideband at fc + fm, and a lower sideband at fc − fm, giving a bandwidth of 2fm. The carrier carries power Pc = Ac²/2, and each sideband adds Pc·m²/4 of useful power — so at 100% modulation (m=1) only 33% of total transmitted power is in the sidebands that carry the information.
In Frequency Modulation (FM), the carrier's instantaneous frequency is shifted by Δf proportional to the message amplitude, while the amplitude stays constant. The FM modulation index β = Δf/fm describes the ratio of the maximum frequency deviation to the message frequency. Carson's rule gives the occupied bandwidth as BW ≈ 2·(Δf + fm), which contains about 98% of the signal power. FM is inherently immune to amplitude noise (since the receiver responds to frequency, not amplitude), which is why broadcast FM sounds cleaner than AM. Commercial FM broadcast in most countries uses Δf = 75 kHz peak deviation and channel spacing of 200 kHz.
Both calculations assume a single sinusoidal message tone; real audio signals are wideband and produce more complex spectra.
Frequently asked questions
m = 1 (Am = Ac). At 100% modulation the amplitude envelope touches zero at troughs and reaches 2Ac at peaks. Going above m=1 (overmodulation) causes clipping and harmonic distortion in the recovered audio and splatter into adjacent channels.
In AM, bandwidth is simply 2·fm regardless of the modulating level. In FM, the bandwidth grows with the frequency deviation: BW = 2·(Δf + fm). Commercial FM broadcast uses Δf = 75 kHz so a 15 kHz audio signal occupies BW ≈ 180 kHz — far wider than an AM station's ~30 kHz for the same audio. The extra bandwidth buys better noise immunity.
Narrowband FM (NBFM) uses a small frequency deviation (β < 1, typically Δf ≈ 5 kHz for voice communications), giving a bandwidth similar to AM. Wideband FM (WBFM) uses large deviation (β ≥ 1, e.g. β ≈ 5 for broadcast FM), giving much better audio fidelity and noise performance at the cost of significantly wider bandwidth.
Also known as
TG we-Calculate Editorial Team. (2026). Modulation Calculator — AM & FM Modulation Index, Bandwidth, Power [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/modulation-calculator
TG we-Calculate Editorial Team. "Modulation Calculator — AM & FM Modulation Index, Bandwidth, Power." TG we-Calculate. 2026. https://we-calculate.com/calculator/modulation-calculator.
TG we-Calculate Editorial Team, "Modulation Calculator — AM & FM Modulation Index, Bandwidth, Power," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/modulation-calculator
@misc{wecalculate_modulation_calculator, title = {Modulation Calculator — AM & FM Modulation Index, Bandwidth, Power}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/modulation-calculator}}, year = {2026}, note = {TG we-Calculate} }
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