Example 1
f = 50 Hz → T = 0.02 s.
Oscillation Period Calculator
Enter frequency in hertz and you get the time of one cycle. Mains at 50 Hz has T = 0.02 s. Two hertz is half a second. Beside that sits ω = 2πf, the same story in radians per second.
The inverse of this card: f = 1/T. ω from period: ω = 2π/T. f from k and m: spring.
Result
Frequency f (Hz). The result shows up here.
How it works
Period and frequency are inverses: T = 1/f. If something repeats 50 times per second, one cycle lasts 0.02 s. At f = 2 Hz the period is 0.5 s. At 1 Hz the cycle is exactly one second. The calculator also computes ω = 2πf, so 50 Hz is about 314 rad/s.
One field: frequency f in hertz. The result T is in seconds. f must be positive. A comma and a period are the same, so 0.5 Hz can be 0,5 and you get T = 2 s.
This is a clean conversion, with no spring model and no pendulum. If you know k and m, compute f on the spring page first, then come back here for T. If you timed a swing, go the other way: f = 1/T on frequency from period.
A 440 Hz tuning fork has T ≈ 0.00227 s. Ten hertz is 0.1 s. 0.2 Hz is five seconds per cycle, a slow sway. 100 Hz is 0.01 s. The numbers are exact, because dividing 1 by f has no hidden constant.
Type f, for example 50, and click Calculate. The result is 0.02 s and ω = 2π·50. To check the inverse, open f = 1/T and type 0.02: you return to 50 Hz.
You can also get ω from the period on angular velocity, with ω = 2π/T. Same ω, different input. A 2.01 s pendulum becomes f ≈ 0.50 Hz here or on f = 1/T next door.
How to use
- Type frequency f in hertz. That is cycles per second, for example 50 for mains or 2 for a slow sway.
- Click Calculate. 50 Hz gives T = 0.02 s. 2 Hz gives 0.5 s. 1 Hz gives exactly 1 s.
- The calculator also shows ω = 2πf. At 50 Hz that is about 314 rad/s. At 1 Hz it is 2π ≈ 6.28 rad/s.
- f must be greater than zero. 0.5 and 0,5 are the same frequency and T = 2 s.
- If you know T instead of f, open frequency from period. Get f from k and m on the spring page, then come back for T.
Formula
T = 1 / f
Also ω = 2πf (rad/s).
Letters in T = 1/f
Period is the reciprocal of frequency: T = 1/f. Mains at 50 Hz has T = 0.02 s; the calculator also shows ω = 2πf ≈ 314 rad/s.
- T
- Time of one cycle in seconds. 50 Hz is 0.02 s; 2 Hz is 0.5 s; 1 Hz is exactly 1 s.
- f
- Frequency in hertz, the only field. Typed 50 here inverts to 0.02 s, not to f = 1/T on the sibling card.
- ω
- Angular frequency 2πf. At 50 Hz mains that is about 314 rad/s, the same fact as T = 0.02 s.
Real-life examples
Example 2
f = 2 Hz → T = 0.5 s.
Example 3
f = 1 Hz → T = 1 s.
Example 4
f = 0.5 Hz → T = 2 s.
Example 5
f = 440 Hz.
Example 6
f = 0.2 Hz → T = 5 s.
Example 7
f = 10 Hz → T = 0.1 s.
Example 8
f = 100 Hz.
Example 9
f = 0.1 Hz → T = 10 s.
Example 10
f = 5 Hz → T = 0.2 s.
Ways to use this calculator
- You turn an f from homework or lab into the time of one cycle.
- You check that T = 0.02 s and f = 50 Hz return to each other on the inverse page.
Frequently asked questions
How long is one 50 Hz mains cycle?
T = 1/50 = 0.02 s. 60 Hz, as in some grids outside Europe, is T ≈ 0.0167 s.
What T at 2 Hz and at 0.5 Hz?
2 Hz is 0.5 s. 0.5 Hz is 2 s. The inverse is exact.
What is the ω beside the result?
ω = 2πf in radians per second. 1 Hz is ≈ 6.28 rad/s. 50 Hz is ≈ 314 rad/s.
Can I type a 440 Hz tuning fork?
Yes. T ≈ 0.00227 s. Same A4 pitch, written as a cycle time.
Where do I compute f when I know T?
On frequency from period, with f = 1/T. The two pages are a pair.
Do I need k or L?
No. Only f enters here. The spring and pendulum pages compute f or T from other data.
Can I type 0.2 Hz with a comma?
Yes. 0,2 and 0.2 mean the same f [Hz], so T = 1/f = 5 s.
What T at 10 Hz and at 5 Hz?
10 Hz is 0.1 s. 5 Hz is 0.2 s. Period is the reciprocal of frequency.
Is a hertz the same as a cycle per second?
Yes. 1 Hz = 1/s. The field wants that unit, not rpm.
How do I get ω from T without this card?
ω = 2π/T on angular velocity. From T = 0.02 s you get the same ω ≈ 314 rad/s.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.