Why does Elliptic give the lowest order?

Elliptic filters place ripple in both the passband and stopband, which allows the transition band to be much sharper per pole. Chebyshev I ripples only in the passband, and Butterworth is maximally flat everywhere — so they need more poles to reach the same stopband attenuation.

What does passband ripple mean?

Passband ripple (Rp, in dB) is the maximum allowed gain variation inside the passband. A value of 0.1 dB means the filter gain stays within ±0.1 dB of 0 dB from DC to the passband edge. Butterworth ripple is 0 dB (monotone), but you must still specify a 3 dB corner.

What is stopband attenuation?

Stopband attenuation (Rs, in dB) is the minimum insertion loss required beyond the stopband edge. A value of 40 dB means signals above Fs are reduced to at most 1% of their input amplitude (20 log10(0.01) = −40 dB).

Does this tool handle highpass, bandpass, or bandstop designs?

The formulas calculate the lowpass prototype order, which is the starting point for all classic IIR types. A bandpass or bandstop filter of the same order requires twice as many poles in the final implementation.

What if Fp equals Fs?

The selectivity ratio k = Fp/Fs would equal 1, making the required order infinite. You must enter Fp strictly less than Fs for a lowpass specification.

Filter Order Calculator

Enter your filter specs (ripple, attenuation, frequencies) and get the minimum order for Butterworth, Chebyshev I, or Elliptic designs.

Filter Specification

Filter Type

Passband

Edge Freq (Hz)

Max Ripple (dB)

e.g. 0.1, 1, 3

Stopband

Edge Freq (Hz)

Min Atten (dB)

e.g. 40, 60, 80

Minimum Filter Order

Enter your filter spec and click Calculate.

All-Type Comparison

Results appear after calculation.

Approximation	Exact N	Min N	Trade-off

Formula reference

Butterworth: N = log(d) / log(1/k) where d = √((10^(Rs/10)−1)/(10^(Rp/10)−1)), k = Fp/Fs

Chebyshev I: N = acosh(d) / acosh(1/k)

Elliptic: N = K(k)·K(√(1−d′²)) / (K(k′)·K(d′)) where k′=√(1−k²), d′=1/d, using complete elliptic integrals K(·)

Summary

This tool computes the minimum integer filter order needed to meet a lowpass filter specification. Enter the passband-edge frequency and maximum allowed ripple, the stopband-edge frequency and required minimum attenuation, then choose Butterworth, Chebyshev Type I, or Elliptic approximation. The result is the smallest order that satisfies all four constraints simultaneously, along with the exact (non-integer) order before rounding.

How it works

Enter the passband-edge frequency (Fp) in Hz and maximum passband ripple in dB.
Enter the stopband-edge frequency (Fs) in Hz and minimum stopband attenuation in dB.
Select the filter type: Butterworth, Chebyshev I, or Elliptic.
The calculator computes the selectivity ratio k = Fp / Fs and the discrimination factor d.
Each approximation formula maps those parameters to an exact (real-valued) order.
The result is rounded up to the nearest integer — the minimum order that meets spec.

Use cases

Determine the simplest IIR filter that meets an audio anti-aliasing requirement.
Compare Butterworth vs Chebyshev vs Elliptic complexity for a given attenuation spec.
Estimate hardware cost (pole count) before committing to a filter topology.
Verify textbook filter design exercises with an instant cross-check.
Choose between filter types when balancing group-delay flatness against roll-off steepness.
Size an analog prototype before applying a bilinear transform for DSP implementation.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu