iBeacon Path Loss and Why Zones Beat Meters

iBeacon Path Loss and Why Zones Beat Meters

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

iBeacon Path Loss and Why Zones Beat Meters

A beacon calibrated to -59 dBm at 1 m and read indoors at path-loss exponent n = 2.5 turns an RSSI of -74 dBm into about 3.98 m and a weaker -84 dBm into 10.00 m. But a routine ±8 dB swing from body blockage or multipath scales every estimate by 2.089 each way, spreading that 3.98 m reading from 1.91 m to 8.32 m. This audit works the formula through and asks whether a single reading can honestly claim a precise distance, or only a reliable near-versus-far zone.

Companion to the chapter BLE App Development on ESP32 — every number here comes from that chapter.

Try

A beacon calibrated to -59 dBm at 1 m and read indoors at path-loss exponent n = 2.5 turns an RSSI of -74 dBm into about 3.98 m and a weaker -84 dBm into 10.00 m . Calculate this case.

Observe

But a routine ±8 dB swing from body blockage or multipath scales every estimate by 2.089 each way, spreading that 3.98 m reading from 1.91 m to 8.32 m . Check shows this.

Explain

That factor-of-two-each-way spread is the whole argument for zone labels: because distance sits in the exponent, every +/-8 dB of ordinary RSSI wobble becomes a /2.09-to-x2.09 swing in meters, so a single reading cannot honestly claim a precise distance -- but it can reliably say "near" versus "far." Check confirms it.

See the relationship before changing it

The figure reads from left to right. The blue input is rssi. The middle card names the page’s rule. The green output is estimated distance. The arrow matters: change the input, apply the rule once, then read the result with its unit.

RSSI changes estimated distance A three-part teaching diagram connects rssi, the rule distance = 10^((-59 - RSSI)/(10 x 2.5)), and estimated distance. INPUT RSSI APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrow. The exponent turns an ordinary dB swing into a large distance swing.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is -74 dBm.

  2. 2

    Name the relationship. distance = 10^((-59 - RSSI)/(10 x 2.5))

  3. 3

    Substitute with units. 10^((-59 - (-74))/25) = 10^0.6 = 3.98 m

  4. 4

    Read the result. Keep the unit beside the value, then use the result only inside the technical boundary below.

Predict, then change rssi

Try Predict how estimated distance responds when rssi moves. Calculate rssi; compare estimated distance with that prediction.

-74 dBm
Chapter baseline
Estimated distance

Observe Return to -74 dBm. Recheck estimated distance with rssi at its chapter value.

Explain The exponent turns an ordinary dB swing into a large distance swing.

Check yourself

What should you do before trusting a moved-slider result?
Answer: Predict its direction, apply the displayed relationship, keep the units, and compare the reset value with the chapter’s worked baseline.
What does this small model leave out?
Answer: Only rssi moves here. The estimated distance calculation excludes field effects listed below.

Honesty note. The estimated distance result holds rssi as the only changing input. It is not a field prediction.

Technical boundaries

Outside the fixed “iBeacon Path Loss and Why Zones Beat Meters” arithmetic are multipath, antenna orientation, body absorption, transmit-power variation, scan-window loss, or environment-specific path-loss changes; “iBeacon Path Loss and Why Zones Beat Meters” therefore reports only its named fixtures.

Ada: The worked example runs two RSSI readings through d = 10^((TxPower - RSSI) / (10n)). Both distances are exact – but the interesting part is what the same formula does to measurement noise, so let me finish that thought numerically.

With TxPower = -59 dBm (calibrated at 1 m) and indoor n = 2.5:

  • At RSSI = -74 dBm: exponent (-59 - (-74)) / (10 x 2.5) = 15 / 25 = 0.6, so d = 10^0.6 = 3.9811 m, about 3.98 m.
  • At RSSI = -84 dBm: exponent (-59 - (-84)) / 25 = 25 / 25 = 1.0, so d = 10^1.0 = 10.00 m.

Now the noise. A +/-8 dB swing from body blockage or multipath scales the estimate by 10^(8/25) = 10^0.32 = 2.089:

  • The 3.98 m reading legitimately spans 3.98 / 2.089 = 1.91 m to 3.98 x 2.089 = 8.32 m.

That factor-of-two-each-way spread is the whole argument for zone labels: because distance sits in the exponent, every +/-8 dB of ordinary RSSI wobble becomes a /2.09-to-x2.09 swing in meters, so a single reading cannot honestly claim a precise distance – but it can reliably say “near” versus “far.”

Every number above is taken from the chapter’s own material and re-derived step by step.