Frequency and Period Calculator: f = 1 / T

Convert between frequency and period.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • f = \frac{1}{T}
  • T = \frac{1}{f}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the frequency: frequency = (1) / (period)
  2. Put the values in (every value in its SI unit): frequency = (1) / (0.02)
  3. The answer: frequency: 50 Hz
  4. The same answer in other units: 0.05 kHz; 5.0e-5 MHz; 3000 rev/min

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Period; Frequency (leave it as it is if this is what you are finding) 50 Hz.

  1. The formula, arranged to find the period: period = (1) / (frequency)
  2. Put the values in (every value in its SI unit): period = (1) / (50)
  3. The answer: period: 0.02 s
  4. The same answer in other units: 20 milliseconds; 20000 microseconds

Common questions

What is the relation between frequency and period?

They are reciprocals. A frequency of 50 Hz has a period of 1/50 = 0.02 s.

How do I convert Hz to rpm?

Multiply by 60. 50 Hz is 3000 revolutions per minute.

What is the period of a 1 kHz wave?

1 millisecond.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school physics text (frequency and period).

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