The oscilloscope "5 times rule" is a sine-wave amplitude rule, not a digital-edge rule: bandwidth should be at least 5x the highest frequency component of interest, which limits measured amplitude error to under ±2% per Tektronix guidance [S1] and the December 11, 2025 Keysight glossary entry [S2].
Engineers conflate it with two separate digital-domain heuristics. The bit-rate rule says scope bandwidth should be 2.5x the digital signal's bit rate so the 5th harmonic of the data fits inside the passband, per Teledyne LeCroy (2015-03) [S5]. The rise-time formula t_r = k / BW, with k = 0.35 for sub-2 GHz Gaussian responses and k up to 0.45 for higher-frequency or flat-response scopes, connects bandwidth to the 10-90% edge you actually see on screen [S5][S6].
What the 5x rule actually guarantees
The rule is anchored to the scope's -3 dB point, defined as the frequency where a sine input is attenuated to 70.7% of true amplitude [S1]. At 1/5 of that bandwidth, the same Gaussian response is down only about 0.04 dB, which is the source of the cited ±2% amplitude figure [S1][S4].
The 5x figure is also where the harmonic content of typical non-sinusoidal signals starts to be safe: choosing bandwidth at 5x the fundamental captures the 5th harmonic with negligible roll-off, which is why Keysight frames it as the "general rule" for the highest frequency component of interest [S2]. Hanmatek's May 1, 2026 write-up repeats the same "at least 5x the highest frequency component" wording for 2026-era buyers [S3]. Tek's own caveat is explicit: as signal speeds increase, hitting 5x may not be practical, and more bandwidth simply buys more accurate reproduction [S1].
3 decision criteria: sine vs digital edge vs clock harmonics
Three criteria tell you which rule to apply, and they are not interchangeable. First, identify the signal class: a single-tone sine or a slowly-modulated carrier belongs to the 5x rule, because amplitude error is the only thing that matters. Second, identify the edge: a digital clock, PWM gate drive, or serial-data line is bounded by t_r, and the BW you need is k / t_r. Third, identify the spectral content: for NRZ serial data, the relevant spectral energy extends to roughly half the bit rate, and the 2.5x bit-rate rule of thumb comes from fitting the 5th harmonic of that half-rate clock inside the scope's passband [S5].
Comparison on a 1 Gb/s signal, where t_r is around 50 ps for a fast edge: 5x rule (vs the 500 MHz fundamental) would call for 2.5 GHz and under-measure the edge; the 2.5x bit-rate rule calls for 2.5 GHz but for harmonic, not edge, reasons; the rise-time formula with k=0.35 calls for 7 GHz, which is the only one of the three that actually resolves the 50 ps edge [S5][S6].
The rise-time formula k / BW in numbers
Tek/Siglent and Teledyne LeCroy converge on the same expression, t_r = k / BW, with k=0.35 for sub-2 GHz Gaussian-response scopes and k up to 0.45 for higher-frequency or flatter-response instruments [S4][S5]. Fluke's worked example: a 2 V p-p sine at 500 MHz has a 10-90% rise time of about 700 ps using the 0.35 rule [S6].
Concretely, a 100 MHz scope (k=0.35) shows a rise time of 3.5 ns; a 200 MHz scope (k=0.35) shows 1.75 ns; a 1 GHz scope (k=0.35) shows 350 ps. Inverting the formula gives the bandwidth you need for a target edge: BW = k / t_r, so measuring a 1 ns edge needs 350 MHz (k=0.35) to 450 MHz (k=0.45), and measuring a 100 ps edge needs 3.5 GHz to 4.5 GHz [S4][S5][S6].
Who the 5x rule is for, and who should skip it
The 5x rule is the right starting point for: power-supply ripple work, audio and ultrasound, low-frequency sensor conditioning, and any measurement where amplitude accuracy on a known-frequency tone matters more than edge fidelity. For power-rail measurements specifically, the 20 MHz bandwidth-limit filter discussion of ripple measurement practice is a more constrained variant of the same amplitude-accuracy logic. [S1]
The 5x rule is the wrong tool for: serial-data compliance (USB, Ethernet, PCIe, MIPI), SiC/GaN gate-drive probing, RF-modulated bursts with broadband content, and any signal where t_r is below roughly 1/BW of the candidate scope. In those cases the rise-time formula or the 2.5x bit-rate rule should drive the spec [S5].
Failure modes and known limits
Three failure modes show up when the 5x rule is misapplied. First, under-sampling the edge: a "5x" scope on a fast digital signal hides the real rise time, because the analog front-end simply cannot follow the slew. Second, ignoring probe loading: a probe with insufficient bandwidth or excessive tip capacitance rolls the edge before it reaches the scope, and no amount of scope BW recovers the original [S1]. Third, sample-rate starvation: Nyquist requires sampling at least 2x BW, but in practice 2.5x to 5x BW is needed for usable time resolution, and oversampling beyond 5x gives diminishing returns [S5].
Tek's own framing is that "higher bandwidth will likely provide more accurate reproduction of a signal," so the 5x rule is a floor, not a ceiling [S1]. When you cannot meet 5x because the signal is genuinely fast, spec the scope to the rise-time formula and accept that the 5x framing no longer applies.
Sourcing and the role of the -3 dB point
All four primary sources (Tektronix, Keysight, Hanmatek, Siglent) state the 5x rule as 5x the highest frequency component of interest, with Tek and Siglent explicitly tying the choice to the under-±2% amplitude error bound [S1][S3][S4]. Teledyne LeCroy's primer is the one that pins the -3 dB point to 70.7% of true amplitude and supplies the k=0.35 default for sub-2 GHz Gaussian responses [S5]. For a more general treatment of the instrument's signal-fidelity role, the oscilloscope fundamentals entry covers the front-end architecture that the bandwidth number is summarising.
Trackable signals: recheck the spec when a scope is marketed at "5x" without stating the k factor (Tek implies k=0.35; LeCroy shows k climbs toward 0.45 for flat responses above 2 GHz), and watch for a 2026/2027 update to the 2.5x bit-rate rule as 224G PAM4 edge rates become routine in compliance work [S1][S5].
Component reference pages worth checking: time relay, and pressure transmitter.