Example 1
T = 2 s → f = 0.5 Hz.
Frequency from Period Calculator
Type period T [s]. The calculator computes f = 1/T: 2 s is 0.5 Hz, 0.02 s is 50 Hz, and a 2.01 s pendulum is about 0.50 Hz, not 2 Hz. Zero seconds does not divide.
The inverse of this card: T = 1/f. ω from the same T: ω = 2π/T. f from k and m: spring.
Result
Period T (s). The result shows up here.
How it works
f = 1/T. You turn a measured swing time into hertz. A 2 s period is half a cycle per second, 0.5 Hz. T = 1 s is 1 Hz. T = 0.02 s, a mains cycle, is 50 Hz. T ≈ 0.00227 s is a 440 Hz tuning fork.
One field: period T in seconds. The result f is in hertz. T must be positive. A comma and a period are the same, so 0.5 s can be 0,5 and you get 2 Hz.
This is the pair of the T = 1/f page. If the teacher gave frequency, go there. If a stopwatch showed the time of ten swings, divide by ten and type the mean T here. ω = 2π/T from the same T lives on angular velocity.
A 1 m pendulum has T ≈ 2.01 s, so f ≈ 0.50 Hz, not 2 Hz. Four seconds per cycle is 0.25 Hz. Five seconds is 0.2 Hz. 0.1 s is 10 Hz. 0.2 s is 5 Hz.
Type T, for example 2, and click Calculate. The result is 0.5 Hz. Check: open oscillation period, type 0.5, and you return to 2 s. A spring that already knows k and m computes f itself and does not need this T.
Paste T from a pendulum or a spring here when you want hertz from a period you already have. Do not mix units: convert milliseconds to seconds. 20 ms is 0.02 s and 50 Hz.
How to use
- Type period T in seconds, the time of one full cycle. The calculator examples are 2 s, or 0.02 s for mains.
- Click Calculate. 2 s gives f = 0.5 Hz. 0.02 s gives 50 Hz. 1 s gives 1 Hz.
- T must be greater than zero. 0.5 and 0,5 are the same period and f = 2 Hz.
- If a stopwatch showed n swings, divide the time by n and type the mean T, not the sum.
- The inverse T = 1/f is on oscillation period. ω from this T lives on angular velocity.
Formula
f = 1 / T
Inverse: T = 1 / f.
f and T in f = 1/T
Frequency from one cycle: f = 1/T. T = 2 s is 0.5 Hz. T = 0.02 s is 50 Hz. A 2.01 s pendulum is about 0.50 Hz.
- f
- Frequency [Hz]. 1/2 = 0.5. 1/0.02 = 50. Pair of T = 1/f on the period page.
- T
- Period of one cycle [s]. 2 s or 0.02 s. T must be positive.
Real-life examples
Example 2
T = 1 s → f = 1 Hz.
Example 3
T = 0.02 s.
Example 4
T = 0.5 s → f = 2 Hz.
Example 5
T = 5 s → f = 0.2 Hz.
Example 6
T = 0.1 s → f = 10 Hz.
Example 7
T = 10 s.
Example 8
T ≈ 0.00227 s.
Example 9
T = 0.2 s → f = 5 Hz.
Example 10
T = 4 s → f = 0.25 Hz.
Ways to use this calculator
- You turn a measured pendulum or spring period into hertz.
- You check the pair: T = 2 s and f = 0.5 Hz return to each other on the inverse page.
Frequently asked questions
What f at T = 2 s and at T = 0.02 s?
At 2 s the frequency is 0.5 Hz. At 0.02 s it is 50 Hz. T = 1 s gives exactly 1 Hz.
What f does a 2.01 s pendulum have?
About 0.50 Hz, not 2 Hz. Two hertz would need T = 0.5 s. The calculator divides one by 2.01.
Is T = 0.00227 s equal to 440 Hz?
Yes, approximately. The calculator with 0.0022727 s returns to A4. 1 / 0.0022727 ≈ 440.
Where do I compute T when I know f?
On the oscillation-period page, with T = 1/f. The two cards are a pair: here the unknown is f, there it is T.
How do I get ω from this T?
On the angular-velocity page: ω = 2π/T. From T = 2 s you get π, about 3.14 rad/s, not hertz alone.
Can I type the time of ten swings?
Divide by 10 first. A 20.1 s sum for 10 cycles is T = 2.01 s and f about 0.50 Hz. Typed 20.1 would be read as one long period.
Can I type 0.5 s with a comma?
Yes. 0.5 and 0,5 are the same T [s] and give f = 2 Hz.
What f at T = 4 s and at T = 5 s?
Four seconds give 0.25 Hz. Five seconds give 0.2 Hz. Longer T, smaller f.
Can I type milliseconds as-is?
No. Convert to seconds. 20 ms is 0.02 s and 50 Hz. Typed 20 would be read as 20 s and 0.05 Hz.
Where does T come from if I have k and m?
Get f on the spring page first, then T = 1/f on oscillation period. Here T is already a given, with no k and no m.
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.