Oscilloscope Bandwidth and Rise Time Calculator
The rise time an oscilloscope and probe will show for a given signal, the error that adds, the bandwidth the signal really contains and the system bandwidth needed to measure it within a chosen error.
Results
The dashed line marks the value you entered.
What this tool does
A scope with a −3 dB bandwidth BW has a rise time of about 0.35 ÷ BW, and rise times add in quadrature: what you see is √(t_signal² + t_scope² + t_probe²), always slower than the truth. A 100 MHz scope has a rise time of 3.5 ns, so on a 2 ns edge it shows about 4 ns. The 0.35 constant holds for a response that rolls off smoothly, as most oscilloscopes do. A fast edge also needs more bandwidth than its repetition rate suggests, about 0.35 ÷ t_r, and the probe counts as part of the chain, so the scope's headline figure is the best case.
Formula
t_r(scope) = 0.35 ÷ BW · t_measured = √(t_signal² + t_scope² + t_probe²) · BW(signal) ≈ 0.35 ÷ t_r
Variables
| Symbol | Meaning | Unit |
|---|---|---|
tr | Rise time of the signal (10–90 %) | ns |
bw | Oscilloscope bandwidth (−3 dB) | MHz |
bp | Probe bandwidth (−3 dB) | MHz |
ee | Rise-time error you can accept | % |
TM | Rise time you will see on the screen | ns |
ER | Error in the measured rise time | % |
BS | Bandwidth the signal itself needs | MHz |
BY | Bandwidth of scope and probe together | MHz |
BN | System bandwidth needed for that error | MHz |
Worked example
- Rise time of the signal (10–90 %)2 ns
- Oscilloscope bandwidth (−3 dB)200 MHz
- Probe bandwidth (−3 dB)300 MHz
- Rise-time error you can accept3 %
- Rise time you will see on the screen2.902 ns
- Error in the measured rise time45.12 %
- Bandwidth the signal itself needs175.0 MHz
- Bandwidth of scope and probe together166.4 MHz
- System bandwidth needed for that error709.1 MHz
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.