Modulation Calculator

How to use this modulation index calculator

What this calculator does

This calculator evaluates the modulation index for three common analog-carrier cases: amplitude modulation (AM), frequency modulation (FM), and phase modulation (PM). The index is a dimensionless measure of how strongly a message signal varies the selected carrier parameter. For AM, it is the ratio of message amplitude to carrier amplitude. For FM, it is the ratio of peak frequency deviation to the message-signal frequency. For PM, the phase modulation index is the peak phase deviation when that deviation is expressed in radians. The result describes modulation depth or excursion; it does not by itself determine receiver quality, legal channel occupancy, spectral purity, or whether a transmitter complies with a particular radio service rule.

When to use it

Use the calculator when checking a laboratory signal generator setup, translating measured carrier and message quantities into a modulation index, comparing how changes in deviation affect FM depth, or verifying a textbook or communications-engineering calculation. It is also useful when preparing a quick design note before applying a fuller bandwidth or spectrum model. For broader context on how information is carried by changing amplitude, frequency, or phase, see NASA JPL's radio-wave modulation lesson.

How to calculate

1. The calculator opens with a complete AM demonstration: 40 V message amplitude and 50 V carrier amplitude. Its result is already calculated, and the example XLSX workbook is immediately available.
2. Choose Amplitude, Frequency, or Phase in Calculate modulation index of. The relevant input fields appear automatically.
3. Replace the demonstration values with your measured or specified values. The result updates live; no separate Calculate button is required.
4. Read Modulation index, then use the Formula and Interpretation cards to confirm which relationship is active and what the value means in that mode.
5. Select Download Excel to export the current validated inputs and result as a real XLSX workbook. Reset clears the demonstration and all numeric data. After Reset, Download Excel is disabled until the currently selected mode again has a complete valid input set.

Input guide

Calculate modulation index of is a required selection with three choices: Amplitude, Frequency, and Phase. Choosing a different mode changes the active formula and which numeric fields are required. A common mistake is mixing quantities from different modulation types, such as entering an FM deviation while the calculator is still in Amplitude mode.

Message signal amplitude (Am) is required in Amplitude mode. Enter a nonnegative decimal number in volts, for example 40. The input accepts standard decimal-point notation and correctly grouped thousands, but not scientific notation or decimal-comma notation. A higher message amplitude raises the AM index in direct proportion. Negative amplitude is rejected because this field represents a peak magnitude.

Carrier signal amplitude (Ac) is required in Amplitude mode and must be greater than zero. Enter volts, for example 50. Increasing the carrier amplitude while keeping the message amplitude fixed lowers the AM index. Do not enter zero: the ratio would be undefined. An AM index above 1 can be calculated, but it corresponds to overmodulation in the conventional sinusoidal-envelope model rather than an ordinary 0-to-100% depth.

Max frequency deviation (Δf) is required in Frequency mode. Enter a nonnegative value in kHz, for example 75. It is the peak departure of the instantaneous carrier frequency from its center value. A larger deviation increases the FM index. Message signal frequency (fm) is also required in Frequency mode and must be greater than zero; enter the highest relevant message frequency in kHz, for example 15. Because the FM index is a ratio, both frequency quantities must use the same unit. The ITU's necessary-bandwidth recommendation shows why deviation and highest modulation frequency are important parameters in practical spectrum calculations.

Peak phase deviation (Δθ) is required in Phase mode. Enter a nonnegative value in radians, for example 1.2. In this model, the PM modulation index equals that peak phase deviation numerically. A larger phase excursion therefore raises the index one-for-one. Do not enter degrees unless you first convert them to radians. NIST's work on controlled phase-modulated RF signals provides a metrology-oriented example of phase modulation expressed through a modulation index.

Output guide

Modulation index is the primary output and is dimensionless. In Amplitude mode it is driven by Message signal amplitude and Carrier signal amplitude; zero means no message-amplitude variation, values from 0 to 1 span 0% to 100% conventional AM depth, and values above 1 indicate overmodulation in the simple envelope model. In Frequency mode it is driven by Max frequency deviation and Message signal frequency; zero means zero deviation, while larger positive values mean a larger frequency excursion relative to the message frequency. In Phase mode it equals Peak phase deviation in radians. The Mode summary pill restates the selected modulation type, the Formula pill and card show the exact active identity, and the Result: dimensionless pill reminds you that the index has no physical unit. The Interpretation card is a concise engineering reading of the current value, not a compliance decision.

Worked example

The startup example uses Amplitude mode with Am = 40 V and Ac = 50 V. The calculator applies μa = Am / Ac = 40 / 50 = 0.8. The first-open Modulation index therefore reads 0.8, which is equivalent to an 80% modulation depth in the conventional AM interpretation. If you change the message amplitude to 20 V while leaving the carrier at 50 V, the index falls to 0.4. If instead you switch to Frequency mode and use Δf = 75 kHz and fm = 15 kHz, the FM modulation index is 5.