Bit per Second
Symbol: bpsWorldwide
O que é um/uma Bit per Second (bps)?
Formal Definition
The bit per second (symbol: bps or bit/s) is the fundamental unit of data transfer rate (also called bit rate or data rate) in digital communications and computing. It represents the number of bits — binary digits, each having a value of 0 or 1 — transmitted or processed per second. One bit per second means that exactly one binary digit is transferred in one second. The unit measures the capacity or throughput of a communication channel, network link, or data processing system.
The bit per second is derived from two base concepts: the bit, defined by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication" as the fundamental unit of information, and the second, the SI base unit of time. While the bit itself is not an SI unit, the bit per second is universally used in telecommunications, networking, and computer science as the standard measure of data transfer speed.
Relationship to Bandwidth and Throughput
In networking, it is important to distinguish between bandwidth (the maximum theoretical data rate of a channel), throughput (the actual achieved data rate), and goodput (the useful data rate excluding protocol overhead). All three are measured in bits per second or its multiples. A 100 Mbps Ethernet connection has a bandwidth of 100 million bits per second, but the actual throughput may be lower due to protocol overhead, collisions, and other factors. The goodput — the rate at which useful application data is delivered — is typically lower still, often 90-95% of throughput for TCP connections under favorable conditions.
Etymology
The Origin of "Bit"
The word "bit" is a portmanteau of "binary digit," coined by John Tukey at Bell Laboratories in 1947. Claude Shannon popularized the term in his groundbreaking 1948 paper, where he established the mathematical foundations of information theory. Shannon credited Tukey with the coinage. The concept of binary representation predates the term by centuries — Gottfried Wilhelm Leibniz described binary arithmetic in 1703 — but the formalization of the bit as a unit of information was Shannon's contribution.
From Baud to Bits Per Second
Before "bits per second" became the standard unit for data rate, the term "baud" (named after Émile Baudot, the French telegraph engineer who invented the Baudot code in 1870) was commonly used. Baud measures the number of symbol changes per second on a communication channel. In early telegraphy and modem communications, where each symbol carried exactly one bit, baud and bits per second were identical. However, as modulation techniques advanced and each symbol began carrying multiple bits, the distinction became critical: a 2,400-baud modem using 16-QAM modulation carries 4 bits per symbol, yielding 9,600 bits per second.
The shift from baud to bits per second as the preferred consumer-facing unit occurred in the 1990s as Internet access became mainstream. Modem speeds were marketed in bps (or kbps), and the term became embedded in public consciousness. Today, "baud" is used primarily by telecommunications engineers discussing physical-layer signaling, while "bits per second" and its multiples are the universal currency of data rate specification.
Precise Definition
Base Unit Definition
One bit per second is defined as the transmission or reception of one binary digit (bit) per second of time. The unit is straightforward and requires no physical standard or reference artifact — it is a count of discrete events (bit transmissions) per unit of time.
Decimal vs. Binary Prefixes
When combined with metric prefixes, bits per second uses decimal (SI) prefixes exclusively in networking and telecommunications:
- 1 kbps (kilobit per second) = 1,000 bps - 1 Mbps (megabit per second) = 1,000,000 bps - 1 Gbps (gigabit per second) = 1,000,000,000 bps - 1 Tbps (terabit per second) = 1,000,000,000,000 bps
This is in contrast to units of data storage, where binary prefixes (kibi-, mebi-, gibi-) are sometimes used to denote powers of 1,024. In data transfer contexts, the prefixes always represent powers of 1,000. There is no ambiguity: 1 Mbps always means exactly 1,000,000 bits per second in networking.
Relationship to Bytes
One byte consists of 8 bits. Therefore, 8 bps = 1 byte per second (B/s). This 8:1 ratio is a frequent source of confusion: an Internet connection rated at 100 Mbps (megabits per second) has a theoretical maximum transfer rate of 12.5 MB/s (megabytes per second). The lowercase "b" denotes bits, while the uppercase "B" denotes bytes — a convention that is critically important but often overlooked in casual usage.
História
Telegraph and Early Communications
The concept of measuring information transfer rate predates the formal definition of the bit. In the 1830s and 1840s, telegraph operators and engineers implicitly measured data rates in words per minute or characters per minute. Samuel Morse's telegraph system of the 1840s could transmit roughly 10 to 15 words per minute, which translates to approximately 10 to 20 bits per second using modern encoding. The Baudot code, developed in 1870, transmitted 5-bit characters and operated at speeds up to 30 words per minute on well-maintained lines.
Shannon's Information Theory
The formalization of the bit as a unit of information by Claude Shannon in 1948 provided the theoretical framework for measuring data rates. Shannon's channel capacity theorem established the maximum rate at which information can be reliably transmitted over a noisy channel: C = B × log₂(1 + S/N), where C is the capacity in bits per second, B is the bandwidth in hertz, and S/N is the signal-to-noise ratio. This theorem, known as the Shannon-Hartley theorem, remains the fundamental limit governing all digital communications.
The Modem Era
The practical importance of bits per second exploded with the development of modems for computer communications. The Bell 103 modem (1962) operated at 300 bps. Subsequent generations increased speeds dramatically: 1,200 bps (1977), 2,400 bps (1984), 9,600 bps (1990), 14,400 bps (1991), 28,800 bps (1994), 33,600 bps (1996), and finally 56,000 bps (1998) with V.90 modems. Each generation pushed closer to Shannon's theoretical limit for telephone-grade lines.
Broadband and Beyond
The transition from dial-up to broadband in the late 1990s and 2000s moved common data rates from kilobits to megabits per second. DSL and cable modems initially offered 256 kbps to 1.5 Mbps, then scaled to tens and hundreds of megabits. Fiber optic connections brought gigabit speeds to consumers starting around 2010. Today, backbone network links operate at 100 Gbps to 400 Gbps per wavelength, and research systems have demonstrated throughputs exceeding 1 petabit per second (10¹⁵ bps) over fiber optic cables.
Uso atual
Internet and Broadband
Bits per second and its multiples are the universal language of Internet speed. Internet service providers (ISPs) advertise connection speeds in Mbps or Gbps: typical residential broadband ranges from 25 Mbps (the US FCC's minimum broadband definition as of 2024) to 1 Gbps or more for fiber connections. Speed test services like Ookla's Speedtest report results in Mbps. Streaming video services specify minimum requirements in Mbps: standard definition requires about 3-5 Mbps, HD requires 5-25 Mbps, and 4K UHD requires 25-50 Mbps depending on the codec.
Networking Equipment
All networking equipment is rated in bits per second. Ethernet standards define speeds at 10 Mbps (10BASE-T), 100 Mbps (Fast Ethernet), 1 Gbps (Gigabit Ethernet), 10 Gbps, 25 Gbps, 40 Gbps, 100 Gbps, and 400 Gbps. Wi-Fi generations are similarly characterized: Wi-Fi 4 (802.11n) supports up to 600 Mbps, Wi-Fi 5 (802.11ac) up to 3.5 Gbps, Wi-Fi 6 (802.11ax) up to 9.6 Gbps, and Wi-Fi 7 (802.11be) up to 46 Gbps — though real-world speeds are invariably lower.
Telecommunications
Mobile network generations are defined by their peak data rates. 3G (HSPA+) offered up to 42 Mbps, 4G LTE up to 300 Mbps (LTE-Advanced up to 1 Gbps), and 5G targets peak rates of 20 Gbps with typical user-experienced rates of 100-300 Mbps. Satellite internet services like Starlink deliver 25-200 Mbps to residential customers. Submarine fiber optic cables forming the Internet's backbone carry multiple terabits per second across ocean floors.
Media and Streaming
Digital media encoding relies on bit rates. Audio codecs specify quality in kbps: MP3 at 128 kbps (standard quality) to 320 kbps (high quality), AAC at 96-256 kbps. Lossless audio (FLAC, ALAC) typically runs 800-1,400 kbps. Video bit rates are higher: H.264 at 5-20 Mbps for HD, H.265/HEVC at 3-15 Mbps for equivalent quality, and AV1 achieving similar quality at 2-10 Mbps.
Everyday Use
Internet Speed Tests
The most common encounter with bits per second in daily life is the Internet speed test. When running a speed test on a smartphone or computer, results are reported in Mbps — download speed, upload speed, and sometimes latency. A result of "150 Mbps download / 20 Mbps upload" means the connection can receive 150 million bits per second and send 20 million bits per second. Understanding these numbers helps consumers evaluate their ISP's performance and choose appropriate plans for their usage patterns.
Streaming and Downloads
Bit rate directly affects streaming quality. When a streaming service like Netflix or YouTube automatically adjusts video quality, it is adapting the bit rate to match available bandwidth. Viewers might notice this as a resolution change: a sudden shift from crisp HD to blocky low resolution indicates the available bps has dropped below the required threshold. Music streaming services offer quality tiers defined by bit rate: Spotify's "Normal" is 96 kbps, "High" is 160 kbps, and "Very High" is 320 kbps.
File Transfer Times
Bits per second determine how long file transfers take. To estimate download time, divide the file size in bits by the connection speed in bps. A 4 GB movie (32 gigabits) on a 100 Mbps connection takes approximately 320 seconds (about 5.3 minutes) under ideal conditions. This calculation explains why a "fast" gigabit connection can download the same file in about 32 seconds. Understanding the bit-byte distinction is essential: file sizes are in bytes (B) while speeds are in bits (b), so you must multiply file size by 8 or divide speed by 8 when comparing.
Gaming and Video Calls
Online gaming requires relatively low bandwidth — typically 3-6 Mbps — but demands consistent, low-latency connections. Video conferencing is more bandwidth-intensive: a standard Zoom call uses 1.5-3 Mbps, while a group call can require 3-8 Mbps. When multiple household members stream, game, and video-call simultaneously, total bandwidth requirements add up, making connection speed in Mbps a practical household concern.
In Science & Industry
Information Theory
In information theory, the bit per second serves as the fundamental measure of channel capacity — the maximum rate at which information can be reliably communicated. Shannon's channel capacity theorem (C = B log₂(1 + S/N)) expresses the theoretical maximum in bits per second as a function of bandwidth and signal-to-noise ratio. This theorem has guided the design of every digital communication system since 1948. Modern coding techniques like turbo codes and LDPC (Low-Density Parity-Check) codes approach within fractions of a decibel of the Shannon limit, achieving near-theoretical-maximum bps over real channels.
Network Performance Research
Research in computer networking relies heavily on precise measurement of data rates in bits per second. Network researchers measure throughput, latency, jitter, and packet loss to characterize network performance. Tools like iperf3 measure TCP and UDP throughput in bps between endpoints. Academic papers on network protocols, congestion control algorithms, and routing optimizations report their results in bits per second or its multiples, allowing direct comparison across studies and implementations.
Signal Processing and Telecommunications
In digital signal processing, bit rate is linked to sampling rate and bit depth. The Nyquist theorem dictates that a signal must be sampled at twice its highest frequency to be accurately represented. CD-quality audio (44.1 kHz sampling, 16-bit depth, 2 channels) produces a raw data rate of 1,411,200 bps (1.4112 Mbps). Understanding the relationship between analog signal parameters and digital bit rates is fundamental to audio engineering, video compression, and telecommunications system design.
Multiples & Submultiples
| Name | Symbol | Factor |
|---|---|---|
| Bit per second | bps | 1 |
| Kilobit per second | kbps | 1000 |
| Megabit per second | Mbps | 1000000 |
| Gigabit per second | Gbps | 1000000000 |
| Terabit per second | Tbps | 1000000000000 |
Interesting Facts
Claude Shannon's 1948 paper, which formalized the bit as a unit of information, is widely considered the founding document of the Information Age. Shannon proved that reliable communication is possible at any rate below the channel capacity in bps, no matter how noisy the channel — a result that surprised many contemporary engineers.
The first transatlantic telegraph cable, completed in 1858, operated at approximately 0.1 bits per second — so slow that Queen Victoria's 98-word congratulatory message to President Buchanan took over 16 hours to transmit. Modern transatlantic fiber optic cables carry over 200 terabits per second.
A single human neuron can fire at a maximum rate of about 1,000 times per second, carrying roughly 1,000 bits per second of information. The entire human optic nerve transmits approximately 10 million bits per second from each eye to the brain.
The fastest Internet speed ever recorded in a laboratory setting exceeded 1.8 petabits per second (1.8 × 10¹⁵ bps) over a single optical fiber, achieved by researchers in 2024 — enough to transfer the entire Netflix library in less than one second.
A 56K modem actually could not achieve 56 kbps in practice. FCC power regulations limited upstream data rates to 33.6 kbps, and the theoretical 56 kbps downstream was only possible under ideal conditions. Most users experienced 40-53 kbps at best.
The voyager 1 spacecraft, now over 15 billion miles from Earth, transmits data at approximately 160 bits per second — slower than a 1960s-era modem. At this rate, a single smartphone photo would take over 8 hours to transmit.
Regional Variations
Global Standard
The bit per second and its decimal multiples (kbps, Mbps, Gbps) are used universally worldwide. Unlike many physical units that have regional variants or competing systems, data transfer rates in bits per second represent a truly global standard. The International Telecommunication Union (ITU), IEEE, and all major standards bodies use bits per second as the base unit for data rate specification.
Notation Variations
While the unit itself is universal, notation conventions vary slightly. The IEEE and most international standards use "bit/s" as the formal symbol. In common usage, "bps" is the most widespread abbreviation. Some publications use "b/s." For multiples, the lowercase "b" is critical: "Mb/s" or "Mbps" means megabits per second, while "MB/s" means megabytes per second — an eightfold difference. Unfortunately, this distinction is frequently lost in consumer marketing and journalism, leading to widespread confusion.
Marketing and Advertising
Internet service providers worldwide advertise speeds in bits per second, though the prefixes and typical values vary by market. In South Korea and Japan, multi-gigabit residential connections are common. In the United States and Europe, 100 Mbps to 1 Gbps is typical for broadband. In developing regions, connections of 5-25 Mbps may be considered adequate. ISPs universally advertise the "up to" maximum speed in Mbps, which may differ substantially from the actual throughput experienced by users.
Bits vs. Bytes Confusion
The single greatest source of regional (and universal) confusion regarding data rates is the bit/byte distinction. File sizes are conventionally expressed in bytes (KB, MB, GB), while network speeds are in bits (kbps, Mbps, Gbps). A user with a 100 Mbps connection downloading a 1 GB file may expect it to take 10 seconds, when in fact it takes approximately 80 seconds (8 gigabits ÷ 100 Mbps). Some European ISPs have begun advertising speeds in MB/s to reduce this confusion, but the practice remains inconsistent.