NB-IoT Calculator

The NB-IoT Calculator helps wireless communication engineers, IoT developers, cellular network planners, embedded system designers, researchers, and students analyse the physical layer (PHY) characteristics of Narrowband Internet of Things (NB-IoT) networks defined by the 3GPP standard. By entering the subcarrier spacing and cyclic prefix, the calculator determines useful symbol duration (Tu), total symbol duration (Ts), symbol rate, cyclic prefix overhead, occupied bandwidth, subcarriers per resource block, slot duration, transmission mode, and other important OFDM parameters. It supports the two standard NB-IoT subcarrier spacings of 15 kHz and 3.75 kHz used for low-power wide-area (LPWA) communication in LTE and cellular IoT networks. The calculator is valuable for NB-IoT device design, LTE infrastructure planning, smart metering, industrial IoT, asset tracking, smart agriculture, smart cities, and machine-to-machine (M2M) communication.

Enter Subcarrier Spacing (Δf), Cyclic Prefix (Engineering Override) exactly in the units shown by this nb-iot. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.

• Subcarrier Spacing (Δf) — use kHz.
• Cyclic Prefix (Engineering Override) — use µs.

The results describe the calculated nb-iot values for the inputs you entered. Check each value against the available space, selected components, feed system, and operating conditions before making a final design decision.

The NB-IoT uses Tu = 1/Δf, Ts ≈ Tu + Tcp, Symbol Rate = Δf, Subcarriers = 180 kHz / Δf. Supply Subcarrier Spacing (Δf) (kHz), Cyclic Prefix (Engineering Override) (µs) in the displayed units, then use the calculated values as the first engineering target for this wireless communication design or analysis.

This calculator is based on the 3GPP NB-IoT physical layer specification and the mathematical relationships used in OFDM communication systems. The useful OFDM symbol duration is calculated using Tu = 1 ÷ Δf, where Δf is the subcarrier spacing. Because symbol duration is inversely proportional to subcarrier spacing, a 3.75 kHz subcarrier produces a much longer symbol than a 15 kHz subcarrier. A cyclic prefix (CP) is then added to the useful symbol to create the total symbol duration using Ts = Tu + Tcp. The cyclic prefix acts as a guard interval that reduces inter-symbol interference (ISI) caused by multipath propagation. The symbol rate is equal to the selected subcarrier spacing expressed in symbols per second. NB-IoT occupies a single Physical Resource Block (PRB) with a fixed bandwidth of 180 kHz. The number of subcarriers inside that PRB is determined by dividing the occupied bandwidth (180 kHz) by the selected subcarrier spacing. For example, a 15 kHz spacing provides 12 subcarriers, while a 3.75 kHz spacing provides 48 narrowband subcarriers for single-tone uplink transmission. The calculator also estimates cyclic prefix overhead, slot duration, transmission type, and PHY operating mode according to standard NB-IoT configurations. These equations provide an accurate engineering foundation for analysing OFDM timing, spectral efficiency, and physical layer behaviour before practical implementation.

Use the calculated PHY parameters as the engineering reference when designing NB-IoT modems, LTE base stations, embedded firmware, or IoT communication systems. Verify timing synchronisation, subcarrier spacing, occupied bandwidth, and cyclic prefix configuration against the applicable 3GPP release before deployment. During RF validation, measure occupied bandwidth, EVM (Error Vector Magnitude), frequency error, adjacent channel leakage ratio (ACLR), receiver sensitivity, timing synchronisation, and spectrum occupancy using a vector signal analyser (VSA), spectrum analyser, or vector signal generator. Network simulations using MATLAB 5G Toolbox, Keysight SystemVue, Keysight PathWave, NS-3, or other cellular simulation tools are recommended to evaluate PHY-layer performance, latency, coverage, and power consumption under realistic propagation conditions.