Rise Time to Bandwidth Calculator
Convert signal rise time (Tr) into system bandwidth using the standard RC/Gaussian approximation: BW ≈ 0.35 / Tr.
What the rise time to bandwidth calculator does
The rise time to bandwidth calculator converts the 10% to 90% rise time of a signal or a system into its −3 dB bandwidth. Enter the rise time in seconds, in plain or scientific notation such as 1e-9 for one nanosecond, and press Calculate. The result is the bandwidth in hertz using the standard approximation for single-pole and Gaussian responses.
The formula
BW ≈ 0.35 / tr
The constant comes from the step response of a first-order RC low-pass filter. Its output goes from 10% to 90% in tr = 2.2 × RC, and its −3 dB bandwidth is 1 / (2π × RC). Combining the two gives BW × tr = 2.2 / 2π = 0.35. Systems with a Gaussian frequency response, which describes many oscilloscopes and cables, have almost the same product, 0.34.
Worked examples
| Rise time | Enter as | Bandwidth | Typical case |
|---|---|---|---|
| 1 µs | 1e-6 | 350 kHz | Audio amplifier, slow logic |
| 100 ns | 1e-7 | 3.5 MHz | Op-amp stage, sensor front end |
| 10 ns | 1e-8 | 35 MHz | Microcontroller I/O |
| 1 ns | 1e-9 | 350 MHz | Fast CMOS, USB 2.0 edges |
| 100 ps | 1e-10 | 3.5 GHz | Gigabit SerDes, PCIe |
| 35 ps | 3.5e-11 | 10 GHz | High-speed probes and scopes |
Choosing an oscilloscope
To measure a rise time accurately the instrument needs a bandwidth several times higher than the signal’s. A rule of thumb is scope bandwidth of at least 3 to 5 times the signal’s fundamental, or for edges, a scope rise time no more than a third of the edge being measured. Measured rise time combines with the scope’s own rise time as the root sum of squares: tmeasured = √(tsignal² + tscope²). A 1 ns edge viewed on a 350 MHz scope (tr = 1 ns) reads as 1.41 ns, a 41% error. On a 1 GHz scope (0.35 ns) it reads 1.06 ns.
Digital signals and the “knee” frequency
For digital edges, the bandwidth given here is where the signal’s spectrum starts to roll off. Signal-integrity engineers often use a slightly different figure, the knee frequency fknee = 0.5 / tr, as the highest frequency that must be preserved to keep the edge shape. For a 1 ns edge that is 500 MHz. Either way, the clock rate is not what determines the required bandwidth; the edge speed is. A 10 MHz clock with 1 ns edges needs a 350 MHz path, and its harmonics extend well into the hundreds of megahertz, which is why fast edges cause EMI problems on slow buses.
Cables, PCB traces and filters
Every element in the signal path adds its own rise time, and they combine as root sum of squares. A 300 ps source edge through a cable with 200 ps rise time and a 150 ps input stage arrives at √(300² + 200² + 150²) = 391 ps. Working backwards, if a link must deliver 500 ps edges and the receiver contributes 200 ps, the channel itself needs a rise time under 458 ps, a bandwidth of about 760 MHz. The RC low-pass filter calculator gives the cutoff of a deliberate filter, and the RC time constant calculator relates the same RC to timing.
Common mistakes
- Entering nanoseconds as seconds. 5 ns must be entered as 5e-9. A bare 5 gives 0.07 Hz.
- Using 20% to 80% rise time. The 0.35 constant assumes 10% to 90%. For 20% to 80%, use 0.22 instead.
- Applying it to multi-pole filters. Sharp Butterworth or Chebyshev responses ring and have products from 0.35 up to about 0.5.
- Confusing bandwidth with data rate. A 1 Gb/s NRZ signal has a fundamental of 500 MHz; the bandwidth needed depends on its edges, not the bit rate.
Related tools
The frequency converter switches between Hz, kHz, MHz and GHz. The capacitive reactance calculator shows why parasitic capacitance slows edges, and the LC resonant frequency calculator explains ringing on fast transitions.
External references
Frequently asked questions
Why 0.35 and not 0.5?
0.35 gives the −3 dB bandwidth of a single-pole system. 0.5 gives the knee frequency used in signal-integrity budgets. Both are correct for different purposes.
How do I get rise time from bandwidth?
Rearrange: tr = 0.35 / BW. A 100 MHz scope has a rise time of about 3.5 ns.
Does the formula work for fall time?
Yes. For symmetric systems fall time equals rise time; use whichever is slower.
What rise time does a 1 GHz oscilloscope have?
About 350 ps, though many modern scopes with flatter responses quote 0.4 to 0.45 / BW.
Can I use this for mechanical or thermal systems?
Yes, for any first-order system. A thermometer with a 10 s rise time has a bandwidth of 0.035 Hz.