Counter Frequency Division
fout = fin / 2ⁿ
Quick answer
This calculator solves fout = fin / 2ⁿ for Output Frequency. With Input Frequency 10 MHz, Counter Stages 0.5, the result is 7.071 MHz. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A binary ripple counter divides an input clock frequency by two at each stage, so an n-stage counter divides by 2 to the n. This is the standard way to derive slow clocks from a fast oscillator—generating real-time-clock ticks, baud-rate references, or PWM timebases. The final output is a square wave at the divided frequency.
Variables
- fout — Divided output frequency (Hz)
- fin — Input clock frequency (Hz)
- n — Number of flip-flop (divide-by-2) stages
Practical Notes
For a non-power-of-two divisor use a modulo-N (programmable) counter. Each stage also halves duty-cycle jitter accumulation but adds ripple-propagation delay in asynchronous counters.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| fout | Output Frequency | kHz | Hz, kHz, MHz, GHz |
| fin | Input Frequency | MHz | Hz, kHz, MHz, GHz |
| n | Counter Stages | — | — |
Step by step
- 1. What you know: Input Frequency 10 MHz, Counter Stages 0.5
- 2. The relation: fout = fin / 2ⁿ
- 3. Substitute: fin = 10 MHz, n = 0.5
- 4. Result: Output Frequency = 7.071 MHz
Worked examples
Minimum range
Given: Input Frequency 100 kHz, Counter Stages 0.025
Result: Output Frequency = 98.28 kHz
Low range
Given: Input Frequency 1 MHz, Counter Stages 0.25
Result: Output Frequency = 0.8409 MHz
Typical
Given: Input Frequency 10 MHz, Counter Stages 0.5
Result: Output Frequency = 7.071 MHz
High range
Given: Input Frequency 100 MHz, Counter Stages 0.8
Result: Output Frequency = 57.43 MHz
Maximum range
Given: Input Frequency 1 GHz, Counter Stages 8
Result: Output Frequency = 3.906 MHz
Solving for each variable
Solve for Output Frequency
Input Frequency 100 kHz, Counter Stages 0.025 → 98.28 kHz
Solve for Input Frequency
Output Frequency 100 Hz, Counter Stages 0.025 → 101.7 Hz
How Output Frequency changes with Input Frequency
| Input Frequency (input) | Output Frequency (result) |
|---|---|
| 1 MHz | 0.7071 MHz |
| 2.5 MHz | 1.768 MHz |
| 5 MHz | 3.536 MHz |
| 7.5 MHz | 5.303 MHz |
| 10 MHz | 7.071 MHz |
| 15 MHz | 10.61 MHz |
| 20 MHz | 14.14 MHz |
| 40 MHz | 28.28 MHz |
| 70 MHz | 49.5 MHz |
| 100 MHz | 70.71 MHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 7071000 |
| kHz | 7071 |
| MHz | 7.071 |
| GHz | 0.007071 |
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<p><a href="https://vbatpower.com/formulas/counter-frequency-division/">Counter Frequency Division</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Counter Frequency Division?
Use fout = fin / 2ⁿ. With Input Frequency 10 MHz, Counter Stages 0.5, Output Frequency works out to 7.071 MHz.
What is the formula for Counter Frequency Division?
The formula is fout = fin / 2ⁿ. A binary ripple counter divides an input clock frequency by two at each stage, so an n-stage counter divides by 2 to the n.
How do you find Input Frequency when you know the other values?
Rearrange for Input Frequency: with Output Frequency 100 Hz, Counter Stages 0.025, Input Frequency is 101.7 Hz.
What units does Counter Frequency Division use?
Output Frequency is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Digital Logic formulas →Need more features?
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