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Hidden Formulas Send Mixed Signals on Cellphones

More bars in more places? As Apple Inc. AAPL 0.96 % 's blunder with its iPhone signal-strength display revealed, the number of bars on a phone has more to do with the whims of handset manufacturers than it does with hard calculations about network coverage.

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There is no standard industry definition of what the number of signal bars shown on a cellphone should represent. Consumers who switch from one model or brand to another might find that the maximum number of bars has changed from four to five, and that seeing a maximum signal means something totally different on the new handset. Many wireless companies and phone manufacturers won't reveal the math they use to convert signal strength to bars, calling the information proprietary. And last week, after some consumers noticed that holding the iPhone a certain way made the number of signal bars decline, Apple disclosed that the formula it has been using was "totally wrong," causing the display to overstate cell signal strength.

"It's just a rough graphical presentation," Branimir Vojcic, professor of engineering and applied science at George Washington University, says of signal bars.

In theory, the bars represent the power of a phone's connection to its wireless network. Only a tiny amount of power is needed to complete a call or download data, yet most phones will get reception over a wide range of signal strength. A strong signal, obtained for example when a caller is standing near a cell tower, could be about 10 billionths of a watt, according to wireless engineers. (Thus it would take 10 billion such connections to power a 100-watt light bulb.) At the other end of the spectrum, a signal of 10 quadrillionths, or 0.00000000000001, of a watt (a quadrillion is a million billion) could be enough to complete a call. So a phone could still work when it shows one bar, even though it has one-millionth—and not one-fifth—the signal strength of that same phone when it shows five bars.


That one bar of signal strength might suffice, but it could lead to dropped calls, poor data transfers and other cellphone headaches. Cellphone users' ability to interpret the signal bars has been hampered by companies' varying definitions and a lack of full transparency about what the bars mean.

Apple hasn't disclosed details of the calculations it used or the new formula it plans to adopt based on the recommendations of its U.S. network provider AT&T Mobility, the wireless unit of AT&T. (An AT&T spokesman referred questions to Apple, and an Apple spokeswoman didn't respond to a request for comment.) Several tech enthusiasts, though, have tested their iPhones and reported that the company was showing four bars out of a maximum of five even with relatively weak signals. For instance, tech Web site AnandTech reported that signal strength as low as 80 quadrillionths of a watt corresponded to four bars., an independent website for all things iPhone, ran separate tests and concluded that four bars could correspond to signal strength as low as 13 quadrillionths of a watt.

The Google Android, by contrast, shows three bars out of four only when signal strength is above 200 quadrillionths of a watt. That is roughly 2.5 to 16 times stronger than the threshold for iPhone to show four bars out of five.

Comparing the iPhone's formula with other devices is difficult because most manufacturers don't share their calculations either. The Android's software is available on the Internet, but representatives for Motorola Inc., Samsung Electronics Co., Research in Motion Inc. and Nokia Corp. NOK -0.82 % all declined to disclose the formula their handsets use or didn't respond to requests for the information. Representatives for the four major U.S. carriers—AT&T, Verizon Wireless, Sprint Nextel Corp. S 1.06 % and Deutsche Telekom AG's T-Mobile USA—also declined to share formulas, with some saying it was left up to the handset makers.

"This was an extreme example," Simon Saunders, director of technology for Real Wireless Limited, a consultancy in Pulborough, U.K., says of Apple's misleading signal bars. He says he understands why a cellphone maker would show the maximum number of bars for all but the weakest signals. "For the majority of that range, everything sounds the same to you," Dr. Saunders says. The problem with that approach is that the consumer wouldn't know that a call is at risk of being dropped, something that is more likely with weaker reception.

Even the raw signal-strength number doesn't tell wireless users everything they need to know about reception. Other factors—such as interference with other cell towers, the type of wireless network and how many others are using the network—also are important. "The reasons calls get dropped are much more varied than simple signal strength," says Spencer Webb, president of AntennaSys Inc., an antenna-design company in Pelham, N.H. "We have done nothing to make this whole thing more quantitative."

Representatives for the Federal Communications Commission and CTIA, the wireless-industry trade group, say they have no rules or standards for signal bars. Matt Larson, marketing manager for, which sells antennas to boost cellphone signals, says he would like to see that change. "What if your battery indicator said it was full and all of a sudden it dropped to zero?" Mr. Larson asks.

Write to Carl Bialik at

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