Example 1
440 Hz and 880 Hz -> 12.00 semitones.
Semitones between two frequencies calculator
Type two frequencies. The calculator computes k = 12 × log2(f2/f1) and cents beside it. 440 and 880 is a clean 12 semitones. 440 and 660, a just fifth 3:2, is 7.02, not 7.
Raw quotient: frequency ratio. Cents to semitones: cents converter. Start from A4: note frequency.
Result
Enter a value. The result shows up here.
How it works
In equal temperament the semitone count between two tones is twelve times the base-2 log of f2/f1. An octave, ratio 2, gives k = 12. A unison, f2 = f1, gives 0. Two octaves, 110 Hz to 440 Hz, give 24. That is the same grid that multiplies by 2^(k/12) on the transposition page.
A just fifth 3:2 does not land on 7. 660/440 = 1.5, and 12 × log2(1.5) ≈ 7.02 semitones, about 702 cents. The 12-TET fifth is 2^(7/12) and about 659.26 Hz from A4. The pair 440 and 659.26 returns 7.00. The gap of about 2 cents is what lets twelve fifths close the octaves.
When f2 sits below f1, k is negative. 880 Hz down to 440 Hz is minus 12, not a form mistake. 440 and 415.30 Hz give −1.00, a semitone down. Both frequencies must be positive: a log of zero or a negative has no place here.
Cents are semitones times 100. The second card shows them to one decimal, the first keeps two decimals in semitones. 440 and 466.16 Hz is 1.00 semitone, one hundred cents. This is not a microphone tuner: you compute two typed numbers.
Type f1, then f2, click Calculate. A comma and a period work in both fields. If you want the raw quotient without a log, open frequency ratio. If you already have cents from a tuner, convert them on the cents page.
To go the other way, take k and a base on transposition: 440 and k = 7 give you that 659.26 Hz. Or start from A4 on note frequency when the base should stay 440.
How to use
- Type f1 in hertz, for example 440.
- Type f2, for example 880 for an octave or 660 for a just fifth.
- Click Calculate. 440 and 880 give 12.00 semitones and 1200 cents. 440 and 660 give 7.02 and about 702 cents.
- When f2 is lower, the sign is a minus. 880 to 440 is −12.00.
- For the quotient without semitones, open frequency ratio. To shift by this k, open transposition.
Formula
k = 12 × log2(f2 / f1)
Cents = k × 100. Both frequencies > 0. Negative k is correct when f2 sits below f1.
Hz and cents between two pitches
Here k = 12 × log2(f2/f1). 440 and 880 are exactly 12 semitones. 440 and 660, a just fifth 3:2, is 7.02, not 7. Cents = k × 100.
- Hz
- The f1 and f2 pair in hertz. 440 and 880 give k = 12. When f2 sits under f1, k is negative. Both inputs must be positive.
- Cents
- k × 100 on the second tile. 12 semitones is 1200 cents. 7.02 from 440/660 is about 702, not a clean tuner 700.
Real-life examples
Example 2
440 Hz and 660 Hz -> 7.02 semitones, not 7.
Example 3
220 Hz and 440 Hz -> 12.00 semitones.
Example 4
440 Hz and 440 Hz -> 0.00, the same pitch.
Example 5
440 Hz and 466.16 Hz -> 1.00 semitone.
Example 6
440 Hz and 415.30 Hz -> -1.00 semitone.
Example 7
440 Hz and 659.26 Hz -> 7.00 semitones.
Example 8
110 Hz and 440 Hz -> 24.00 semitones.
Ways to use this calculator
- You check how many semitones split two analyzer peaks before you draw the interval on a keyboard.
- You compare a just fifth 3:2 (7.02) with a tempered fifth (7.00 at 659.26 Hz).
- You flip direction: 880 to 440 confirms minus 12 before you drop an oscillator an octave.
Frequently asked questions
How many semitones sit between 440 and 880 Hz?
A clean 12.00, or 1200 cents. That is an octave. 220 to 440 also gives 12.00.
Why are 440 and 660 Hz 7.02, not a flat 7?
660/440 is a just fifth 3:2. In 12-TET a fifth is 2^(7/12), about 659.26 Hz. The gap is about 2 cents.
What do I get at 440 and 659.26 Hz?
7.00 semitones and 700 cents. That is the grid fifth, not 3:2.
What happens when the second frequency is lower?
k comes out negative. 880 Hz to 440 Hz is minus 12. 440 and 415.30 Hz is −1.00.
How many semitones between 440 and 466.16 Hz?
1.00, one hundred cents. 466.16 Hz is A4 plus one semitone in 12-TET.
What is 110 Hz to 440 Hz?
24.00 semitones, two octaves. 440/110 = 4, and 12 × log2(4) = 24.
Do 440 and 440 give zero?
Yes, 0.00 semitones and 0 cents. A unison, the log of 1.
Where is the raw quotient without a log?
On the frequency-ratio page. There 660/440 stays 1.5000.
How do I turn these semitones into new Hz?
Take k and a base on transposition. 440 and 7 give 659.26 Hz.
Does a comma in 466.16 work?
Yes. 466,16 and 466.16 are the same f2. Against 440 the result is 1.00.
Knowledge sources
Frequency and intervals in this calculator follow the hertz and A440 concert pitch.
Page updated in 2026.