Frequency Calculator
Calculate frequency (f), period (T), wavelength (λ), or angular frequency (ω). Supports wave relation (v = fλ), rpm ↔ Hz, smart unit conversions, quick picks, step-by-step work, and a mini frequency scale visual.
Background
Frequency is “how often per second.” It’s linked to period by f = 1/T. For waves, v = fλ. For rotation, Hz = rpm/60. Angular frequency connects via ω = 2πf.
How to use this calculator
- Pick a mode: period ↔ frequency, wave relation, ω ↔ f, or rpm ↔ Hz.
- Enter values and choose units.
- Click Calculate to get clean results + conversions.
- Use Quick picks to sanity-check common cases (50/60 Hz, 440 Hz, rpm records, GHz signals).
How this calculator works
- It converts inputs into base units (Hz, seconds, meters, m/s) to keep calculations consistent.
- Then it applies the relationship for your mode: f = 1/T, v = fλ, ω = 2πf, or Hz = rpm/60.
- Finally, it formats results into student-friendly units (like ms/µs for period, or kHz/MHz/GHz for frequency).
Formula & Equation Used
Frequency and period:
Wave relation:
Angular frequency:
Rotation conversion:
Example Problems & Step-by-Step Solutions
Example 1 — Frequency from period
A signal repeats every 0.02 s. f = 1/T = 1/0.02 = 50 Hz.
Example 2 — Period from frequency
U.S. AC power is 60 Hz. T = 1/f = 1/60 ≈ 0.0167 s = 16.7 ms.
Example 3 — Wave relation
Sound speed is 343 m/s and wavelength is 0.78 m. f = v/λ = 343/0.78 ≈ 440 Hz.
Example 4 — rpm ↔ Hz
A record spins at 33⅓ rpm. Hz = rpm/60 = 33.33/60 ≈ 0.556 Hz.
Frequently Asked Questions
Q: What’s the difference between frequency and angular frequency?
Frequency is in Hz (cycles/s). Angular frequency is in rad/s and equals ω = 2πf.
Q: How do I convert rpm to Hz fast?
Divide by 60: Hz = rpm/60.
Q: When should I use v = fλ?
Use it whenever the problem gives any two of speed, frequency, and wavelength.
