Example 1
440 Hz and 880 Hz -> 2.0000.
Frequency quotient f2/f1 calculator
Type two frequencies [Hz] and read f2 divided by f1. 880 on 440 is 2.0000, a pure octave. 660 on 440 is 1.5000, a just fifth 3:2. Unison, 440 on 440, stays 1.0000.
Semitones from this pair: interval. A shift: Hz transposition. Cents: cents to semitones.
Result
Enter a value. The result shows up here.
How it works
Just intervals are small-number ratios: octave 2:1, fifth 3:2, fourth 4:3, major third 5:4, major second 9:8. Here you get the decimal quotient f2/f1, not a colon pair. 880/440 = 2.0000. 660/440 = 1.5000. 550/440 = 1.2500, that is 5:4.
The quotient f2/f1, for example 660/440 = 1.5. A just fifth stays 1.5000 even though the tempered ratio is 2^(7/12) ≈ 1.4983. If you want semitones and cents, open the interval page. There 440 and 660 give 7.02, not a flat 7.
Both frequencies must be positive. f2 may sit below f1: then the ratio is a fraction under 1. 440 over 880 is 0.5000, an octave down. 330 and 440 give 1.3333, close to a fourth 4:3.
The result has four decimal places so 5:4 (1.2500) and 9:8 (1.1250) do not flatten into a short 1.25. 495/440 = 1.1250. 220 and 880 give 4.0000, two octaves. 200 and 300 are 1.5000 again, the same fifth in other hertz.
Type f1 as the denominator, f2 as the numerator, then Calculate. A comma and a period work in both fields. The calculator does not guess which note is tonic: field order sets the direction.
A generator and an analyzer speak Hz. This quotient tells you whether a pair sits near a just ratio before you lock the 12-TET grid. To shift by a known k semitones, use transposition, not this quotient.
How to use
- Type f1 as the base, for example 440 Hz.
- Type f2, for example 660 Hz for a 3:2 fifth or 880 Hz for an octave.
- Click Calculate. 440 and 880 give 2.0000. 440 and 660 give 1.5000. 440 and 440 give 1.0000.
- When f2 is lower, the result drops below 1. 440 over 880 is 0.5000.
- For semitones from the same pair, open the interval page. There 440 and 660 are 7.02, not 1.5.
Formula
ratio = f2 / f1
Both frequencies > 0. This is a raw quotient, not semitones. Octave = 2, unison = 1.
f1, f2, and the raw quotient
Ratio = f2 / f1. 880 on 440 is 2.0000, a pure octave. 660 on 440 is 1.5000, a just fifth. Unison 440 on 440 stays 1.0000.
- f1
- Denominator frequency [Hz]. 440 under 880 gives 2. Zero hertz does not divide.
- f2
- Numerator frequency [Hz]. 660 on 440 is 1.5000. A lower f2 gives a quotient below 1.
- Hz
- Hertz on both fields. 880/440 and 300/200 give the same 1.5000. Not semitones from 12 × log2.
- octave
- Quotient 2.0000. 880/440 or 440/220. Two octaves is 4.0000, as in 880/220.
Real-life examples
Example 2
440 Hz and 660 Hz -> 1.5000.
Example 3
330 Hz and 440 Hz -> 1.3333.
Example 4
440 Hz and 550 Hz -> 1.2500.
Example 5
440 Hz and 495 Hz -> 1.1250.
Example 6
220 Hz and 880 Hz -> 4.0000.
Example 7
440 Hz and 440 Hz -> 1.0000.
Example 8
200 Hz and 300 Hz -> 1.5000.
Ways to use this calculator
- You check whether two oscillators sit near 3:2 before you lock temperament on the keyboard.
- You compare a harmonic peak with the fundamental: 2 is an octave, 1.5 a fifth, 1.25 a major third.
- You park 4:3 (1.3333) next to 440 and 330 Hz when you tune just, not on the MIDI grid.
Frequently asked questions
What is 880/440 and 660/440?
The quotient is 2.0000 and 1.5000. The first pair is an octave, the second a just fifth 3:2. You compute f2 [Hz] / f1 [Hz].
What quotient is a major third 5:4 and a second 9:8?
550/440 = 1.2500 and 495/440 = 1.1250. The calculator keeps four decimals. A raw quotient, not semitones.
What is 330 Hz to 440 Hz?
The quotient is 1.3333, close to a fourth 4:3. Exact 4/3 is 1.3333 at this four-decimal rounding.
Do 440 and 440 give 1?
Yes, 1.0000. A unison. Direction disappears because numerator and denominator match. f2 / f1 = 1.
What if the second frequency is lower?
The ratio drops below 1. 440/880 = 0.5000, an octave down. Same interval, inverted quotient.
Why is this not 7 semitones at 440 and 660?
Because there is no logarithm here. 1.5000 stays 1.5000. The 7.02 semitones live on the interval page.
What is 220 Hz to 880 Hz?
The quotient is 4.0000, two octaves. Each octave multiplies frequency by 2. 220 Hz to 880 Hz.
Do 200 and 300 Hz also give 1.5?
Yes. 300/200 = 1.5000. Same fifth 3:2, different hertz. The quotient does not depend on how high the pair sits.
What ratio is a tempered fifth from 440?
659.26 / 440 ≈ 1.4983, not 1.5000. The gap is intentional in 12-TET. Here the raw quotient stays.
Does a comma in 261.63 work in both fields?
Yes. 261,63 and 261.63 are the same f [Hz]. A comma and a period are the same hertz.
Knowledge sources
Frequency and intervals in this calculator follow the hertz and A440 concert pitch.
Page updated in 2026.