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Frequency to Period Calculator – Convert Hz to Seconds, ms & ns Instantly

Physics Tool

Frequency to Period Calculator

Convert frequency to period and period to frequency instantly in all time units — seconds, milliseconds, microseconds, and nanoseconds. Works for any frequency from Hz to GHz.

Frequency to Period & Period to Frequency
T = 1 ÷ f
Period from frequency

Frequency and Period Formula

Frequency and period are two fundamental properties of any repeating wave or oscillation. They are exact mathematical inverses of each other, linked by one of the simplest yet most important formulas in physics.

T = 1 ÷ f
Period from frequency
where T = period (seconds), f = frequency (Hz — cycles per second)
f = 1 ÷ T
Frequency from period
where f = frequency (Hz), T = period (seconds)

The Inverse Relationship

Frequency and period have a perfect inverse relationship:

  • Higher frequency = shorter period — more cycles happen per second, so each cycle takes less time
  • Lower frequency = longer period — fewer cycles happen per second, so each cycle takes more time
  • They are exact mathematical inverses: T × f = 1 always
T = 1/f
Period from Frequency
⟷
f = 1/T
Frequency from Period

Worked Examples

Example 1: f = 50 Hz → T in seconds and milliseconds

  1. Given: f = 50 Hz (UK mains electricity)
  2. Apply formula: T = 1/f = 1/50
  3. Calculate: T = 0.02 s
  4. Convert to milliseconds: T = 0.02 × 1,000 = 20 ms

Answer: T = 0.02 s = 20 ms

Example 2: f = 1 kHz = 1,000 Hz → T in ms

  1. Given: f = 1 kHz = 1,000 Hz
  2. Apply formula: T = 1/f = 1/1,000
  3. Calculate: T = 0.001 s
  4. Convert to milliseconds: T = 0.001 × 1,000 = 1 ms

Answer: T = 0.001 s = 1 ms

Example 3: T = 4 ms = 0.004 s → f in Hz

  1. Given: T = 4 ms = 0.004 s
  2. Apply formula: f = 1/T = 1/0.004
  3. Calculate: f = 250 Hz

Answer: f = 250 Hz

How to Convert Hz to Seconds

Converting frequency (Hz) to period (seconds) is a straightforward calculation using the formula T = 1/f. Follow these four steps to convert any frequency to its corresponding period.

Step-by-Step Guide

  1. Step 1: Write down your frequency in Hz
    • If in kHz: multiply by 1,000
    • If in MHz: multiply by 1,000,000
    • If in GHz: multiply by 1,000,000,000
  2. Step 2: Apply the formula T = 1 ÷ f
  3. Step 3: Result is the period in seconds
  4. Step 4: Convert to smaller units if needed:
    • × 1,000 to get milliseconds (ms)
    • × 1,000,000 to get microseconds (µs)
    • × 1,000,000,000 to get nanoseconds (ns)

Complete Worked Examples

Example 1: Convert 100 Hz to milliseconds

  1. Given: f = 100 Hz
  2. Apply formula: T = 1/100
  3. Calculate: T = 0.01 s
  4. Convert to ms: T = 0.01 × 1,000 = 10 ms
  5. Convert to µs: T = 0.01 × 1,000,000 = 10,000 µs
  6. Convert to ns: T = 0.01 × 1,000,000,000 = 10,000,000 ns

Answer: T = 0.01 s = 10 ms = 10,000 µs = 10,000,000 ns

✓ This directly answers "100 hz to ms"

Example 2: Convert 10,000 Hz (10 kHz) to seconds

  1. Given: f = 10,000 Hz = 10 kHz
  2. Apply formula: T = 1/10,000
  3. Calculate: T = 0.0001 s
  4. Convert to ms: T = 0.0001 × 1,000 = 0.1 ms
  5. Convert to µs: T = 0.0001 × 1,000,000 = 100 µs
  6. Convert to ns: T = 0.0001 × 1,000,000,000 = 100,000 ns

Answer: T = 0.0001 s = 0.1 ms = 100 µs = 100,000 ns

✓ This directly answers "10000 hz to seconds"

Example 3: Convert 1 Hz to seconds

  1. Given: f = 1 Hz (one cycle per second)
  2. Apply formula: T = 1/1
  3. Calculate: T = 1 s
  4. Convert to ms: T = 1 × 1,000 = 1,000 ms
  5. Convert to µs: T = 1 × 1,000,000 = 1,000,000 µs

Answer: T = 1 s = 1,000 ms = 1,000,000 µs

✓ This directly answers "1 hz to seconds" and "1 hertz to seconds"

Example 4: Convert 2.4 GHz (WiFi frequency) to nanoseconds

  1. Given: f = 2.4 GHz = 2,400,000,000 Hz = 2.4 × 109 Hz
  2. Apply formula: T = 1/f = 1/(2.4 × 109)
  3. Calculate: T = 4.167 × 10-10 s
  4. Convert to ns: T = 4.167 × 10-10 × 109 = 0.4167 ns
  5. Convert to ps: T = 416.7 ps

Answer: T = 4.167 × 10-10 s = 0.4167 ns = 416.7 ps

Example 5: Convert 440 Hz (musical note A) to milliseconds

  1. Given: f = 440 Hz (concert pitch A above middle C)
  2. Apply formula: T = 1/440
  3. Calculate: T = 0.002273 s
  4. Convert to ms: T = 0.002273 × 1,000 = 2.273 ms

Answer: T = 0.002273 s = 2.273 ms

How to Convert Seconds to Hz

Converting period (seconds) to frequency (Hz) uses the inverse formula f = 1/T. This conversion is essential in electronics, physics, and audio engineering.

Step-by-Step Guide

  1. Step 1: Write down your period in seconds
    • If in ms: divide by 1,000
    • If in µs: divide by 1,000,000
    • If in ns: divide by 1,000,000,000
  2. Step 2: Apply the formula f = 1 ÷ T
  3. Step 3: Result is frequency in Hz
  4. Step 4: Convert to kHz, MHz, GHz as needed

Complete Worked Examples

Example 1: Convert 0.02 s (20 ms) to Hz

  1. Given: T = 0.02 s = 20 ms
  2. Apply formula: f = 1/T = 1/0.02
  3. Calculate: f = 50 Hz

Answer: f = 50 Hz (UK mains electricity frequency)

Example 2: Convert 1 ms to kHz

  1. Given: T = 1 ms = 0.001 s
  2. Apply formula: f = 1/T = 1/0.001
  3. Calculate: f = 1,000 Hz
  4. Convert to kHz: f = 1,000/1,000 = 1 kHz

Answer: f = 1,000 Hz = 1 kHz

Example 3: Convert 1 µs to MHz

  1. Given: T = 1 µs = 0.000001 s = 10-6 s
  2. Apply formula: f = 1/T = 1/(10-6)
  3. Calculate: f = 1,000,000 Hz = 106 Hz
  4. Convert to MHz: f = 1 MHz

Answer: f = 1,000,000 Hz = 1 MHz

Example 4: Convert 5 ms to Hz

  1. Given: T = 5 ms = 0.005 s
  2. Apply formula: f = 1/T = 1/0.005
  3. Calculate: f = 200 Hz

Answer: f = 200 Hz

Frequency vs Period — What is the Difference?

Frequency and period describe the same repeating phenomenon from two different perspectives. Understanding the difference is crucial for anyone working with waves, oscillations, or AC signals.

Property Frequency (f) Period (T)
Definition Number of cycles per second Time for one complete cycle
Symbol f T
SI Unit Hertz (Hz) Seconds (s)
Formula f = 1/T T = 1/f
Higher value means More cycles per second Longer time per cycle
Example 50 Hz = 50 cycles/s 0.02 s = 20 ms per cycle
Relationship f × T = 1 always

Why Frequency and Period Are Inverses

Imagine a wave that completes 10 cycles in 1 second. Its frequency is 10 Hz (10 cycles per second). Since 10 cycles happen in 1 second, each cycle must take 1/10 = 0.1 seconds. That's the period.

The formula f × T = 1 captures this perfectly. If you know one, you can always calculate the other by taking the reciprocal (1 divided by the value).

Real World Examples

Mains Electricity (AC Power):

  • UK/Europe: f = 50 Hz → T = 1/50 = 0.02 s = 20 ms per cycle
  • USA/Canada: f = 60 Hz → T = 1/60 = 0.01667 s = 16.67 ms per cycle
  • This difference affects motor speeds and transformer design across different countries

Musical Notes and Audio:

  • Middle C: f = 261.6 Hz → T = 1/261.6 = 3.82 ms per wave
  • Note A (concert pitch): f = 440 Hz → T = 1/440 = 2.27 ms per wave
  • Human hearing range: 20 Hz (T = 50 ms) to 20 kHz (T = 50 µs)

Computer CPU Clock Speeds:

  • 1 GHz CPU: f = 1 × 109 Hz → T = 1 nanosecond per clock cycle
  • 3.6 GHz CPU: f = 3.6 × 109 Hz → T = 0.278 nanoseconds per cycle
  • Faster CPU = shorter period per cycle = more calculations per second

How to Choose Which Unit to Use

  • Use frequency (Hz) when describing repeating signals, waves, oscillations, or vibrations
  • Use period (s) when measuring the duration of one complete event or cycle
  • In electronics: frequency is more common for AC signals and clock speeds
  • In physics: period is often easier to measure directly with oscilloscopes

Hz to Seconds Conversion Table

This reference table shows pre-calculated period values for common frequencies. Click any row in the interactive table above to automatically fill the calculator with that frequency.

Frequency Period (s) Period (ms) Period (µs) Angular Freq (rad/s) Application
0.1 Hz 10 s 10,000 ms — 0.628 rad/s Slow oscillation
1 Hz 1 s 1,000 ms 1,000,000 µs 6.283 rad/s 1 cycle/second
10 Hz 0.1 s 100 ms 100,000 µs 62.83 rad/s Slow motor
50 Hz 0.02 s 20 ms 20,000 µs 314.16 rad/s UK mains electricity
60 Hz 0.01667 s 16.67 ms 16,667 µs 376.99 rad/s US mains electricity
100 Hz 0.01 s 10 ms 10,000 µs 628.32 rad/s Common reference
440 Hz 0.002273 s 2.273 ms 2,273 µs 2,764.6 rad/s Musical note A
1 kHz 0.001 s 1 ms 1,000 µs 6,283.2 rad/s Audio reference
10 kHz 0.0001 s 0.1 ms 100 µs 62,832 rad/s Upper audio range
1 MHz 10-6 s 0.001 ms 1 µs 6.28 × 106 rad/s Radio/electronics
1 GHz 10-9 s — 0.001 µs 6.28 × 109 rad/s Microwave/CPU
2.4 GHz 4.167 × 10-10 s — — 1.51 × 1010 rad/s WiFi

Frequency and Period in Real Life

Understanding frequency and period is essential across many fields. Here's how these concepts appear in everyday technology and science.

Mains Electricity (AC Power)

UK/Europe: 50 Hz → T = 20 ms per cycle

European electrical grids operate at 50 Hz, meaning the voltage alternates direction 50 times per second. Each complete AC cycle takes exactly 20 milliseconds.

USA/Canada: 60 Hz → T = 16.67 ms per cycle

North American grids operate at 60 Hz. Each cycle takes 16.67 milliseconds. This seemingly small difference affects:

  • Electric motor speeds (motors run 20% faster on 60 Hz)
  • Transformer efficiency and design
  • Clocks that use AC frequency as a timebase
  • Compatibility of electrical equipment between regions

Musical Notes and Audio

Middle C: 261.6 Hz → T = 3.82 ms

When a piano string or vocal cord vibrates at 261.6 Hz, it completes one full vibration cycle every 3.82 milliseconds. This is how our ears perceive the note middle C.

Note A (concert pitch): 440 Hz → T = 2.27 ms

The internationally agreed reference pitch A above middle C vibrates exactly 440 times per second (440 Hz). Orchestras tune to this frequency.

Human hearing range: 20 Hz (T = 50 ms) to 20 kHz (T = 50 µs)

The lowest bass we can hear has a 50 millisecond period. The highest treble we can hear has a 50 microsecond period — 1,000 times faster.

Computer CPU Clock Speeds

1 GHz CPU: T = 1 nanosecond per clock cycle

A 1 GHz processor executes one billion clock cycles per second. Each cycle takes exactly 1 nanosecond (0.000000001 seconds).

3.6 GHz CPU: T = 0.278 nanoseconds per cycle

Modern high-speed CPUs complete over 3.6 billion cycles every second. Each cycle takes just 278 picoseconds. At these speeds, even the speed of light becomes a limiting factor in chip design.

Why period matters: Chip designers must ensure electrical signals can propagate across the entire chip within one clock period. As CPUs get faster (higher frequency, shorter period), physical chip size must shrink.

Radio Waves and WiFi

FM radio 100 MHz: T = 10 nanoseconds

FM radio waves oscillate 100 million times per second. Each electromagnetic wave cycle takes 10 nanoseconds.

WiFi 2.4 GHz: T = 0.417 nanoseconds

WiFi signals at 2.4 GHz complete 2.4 billion oscillations per second. Each wave takes just 417 picoseconds.

WiFi 5 GHz: T = 0.2 nanoseconds

Higher frequency WiFi (5 GHz) has even shorter periods — just 200 picoseconds per wave. This shorter wavelength allows more data transmission but has reduced range through walls.

Medical and Scientific Applications

ECG heartbeat: ~1.2 Hz (T ≈ 833 ms) at 72 bpm

A resting heart rate of 72 beats per minute equals 1.2 beats per second (1.2 Hz). Each heartbeat cycle takes about 833 milliseconds.

Ultrasound imaging: 1–20 MHz (T = 0.05–1 µs)

Medical ultrasound uses high-frequency sound waves (1 to 20 million cycles per second) to create images. Each sound wave cycle takes between 50 nanoseconds and 1 microsecond.

MRI Larmor frequency: ~64 MHz at 1.5T

In a 1.5 Tesla MRI scanner, hydrogen atoms resonate at about 64 MHz. This means each precession cycle takes approximately 15.6 nanoseconds. The exact frequency depends on magnetic field strength.

Angular Frequency Calculator — ω from Hz

Angular frequency (ω, omega) measures oscillation speed in radians per second instead of cycles per second. It's widely used in physics, engineering, and electronics because it simplifies many mathematical equations involving oscillations and waves.

ω = 2πf
Angular frequency (rad/s) = 2π × frequency (Hz)
ω = 2π ÷ T
Angular frequency from period

Why multiply by 2π? One complete cycle covers 2π radians (360 degrees). So if something oscillates at f Hz (f cycles per second), it sweeps through 2πf radians per second.

Worked Examples: Angular Frequency

Example 1: f = 50 Hz → ω in rad/s

  1. Given: f = 50 Hz (UK mains frequency)
  2. Apply formula: ω = 2πf = 2π × 50
  3. Calculate: ω = 314.16 rad/s

Answer: ω = 314.16 rad/s

This is the angular frequency of AC power in Europe. The voltage completes 314.16 radians of rotation per second.

Example 2: f = 1 kHz → ω in rad/s

  1. Given: f = 1 kHz = 1,000 Hz
  2. Apply formula: ω = 2πf = 2π × 1,000
  3. Calculate: ω = 6,283.2 rad/s

Answer: ω = 6,283.2 rad/s

Example 3: T = 0.01 s → ω in rad/s

  1. Given: T = 0.01 s (period of 100 Hz signal)
  2. Apply formula: ω = 2π/T = 2π / 0.01
  3. Calculate: ω = 628.32 rad/s

Answer: ω = 628.32 rad/s

Where Angular Frequency Is Used

  • AC Circuit Analysis: ω simplifies impedance calculations for capacitors (Z = 1/ωC) and inductors (Z = ωL)
  • Wave Equations: y = A sin(ωt) describes oscillating systems more cleanly than y = A sin(2πft)
  • Simple Harmonic Motion: Springs, pendulums, and oscillators use ω in their equations of motion
  • Signal Processing: Fourier analysis and filter design rely heavily on angular frequency

Worked Examples

Here are detailed step-by-step solutions to common frequency and period conversion problems.

1. How to convert 100 Hz to milliseconds

Solution:

  1. Given: f = 100 Hz
  2. Formula: T = 1/f
  3. Calculate: T = 1/100 = 0.01 s
  4. Convert to milliseconds: T = 0.01 × 1,000 = 10 ms

Answer: 10 ms — Each cycle of a 100 Hz wave takes exactly 10 milliseconds.

2. How to convert 10,000 Hz to seconds

Solution:

  1. Given: f = 10,000 Hz = 10 kHz
  2. Formula: T = 1/f
  3. Calculate: T = 1/10,000 = 0.0001 s
  4. In scientific notation: T = 1 × 10-4 s = 100 µs

Answer: 0.0001 s = 100 µs

3. How to convert 1 Hz to seconds

Solution:

  1. Given: f = 1 Hz (definition: one cycle per second)
  2. Formula: T = 1/f
  3. Calculate: T = 1/1 = 1 s

Answer: 1 second — By definition, 1 Hz means exactly one complete cycle takes one second.

4. How to convert 2.4 GHz to nanoseconds

Solution:

  1. Given: f = 2.4 GHz = 2.4 × 109 Hz = 2,400,000,000 Hz
  2. Formula: T = 1/f
  3. Calculate: T = 1/(2.4 × 109) = 4.167 × 10-10 s
  4. Convert to nanoseconds: T = 4.167 × 10-10 × 109 = 0.4167 ns
  5. Or in picoseconds: T = 416.7 ps

Answer: 0.4167 ns = 416.7 ps — WiFi signals at 2.4 GHz oscillate incredibly fast.

5. How to convert 20 ms to Hz

Solution:

  1. Given: T = 20 ms = 0.02 s
  2. Formula: f = 1/T
  3. Calculate: f = 1/0.02 = 50 Hz

Answer: 50 Hz — This is the frequency of UK/European mains electricity.

6. How to convert 1 µs period to MHz

Solution:

  1. Given: T = 1 µs = 1 × 10-6 s = 0.000001 s
  2. Formula: f = 1/T
  3. Calculate: f = 1/(1 × 10-6) = 1 × 106 Hz
  4. Convert to MHz: f = 1 MHz

Answer: 1 MHz — A 1 microsecond period corresponds to 1 megahertz.

7. What is the period of 440 Hz?

Solution:

  1. Given: f = 440 Hz (musical note A)
  2. Formula: T = 1/f
  3. Calculate: T = 1/440 = 0.002273 s
  4. Convert to milliseconds: T = 2.273 ms

Answer: 2.273 ms — Each vibration of concert A takes 2.273 milliseconds.

8. How to convert sec to Hz step by step

General method:

  1. Write your period T in seconds (convert from ms/µs/ns if needed)
  2. Use formula: f = 1 ÷ T
  3. The result is frequency in Hz
  4. Convert to kHz (÷1000), MHz (÷1,000,000), or GHz (÷1,000,000,000) as needed

Example: T = 0.005 s → f = 1/0.005 = 200 Hz

9. How to find frequency from period in ms

Solution:

  1. Convert milliseconds to seconds: divide by 1,000
  2. Example: T = 5 ms = 5/1,000 = 0.005 s
  3. Apply formula: f = 1/T = 1/0.005 = 200 Hz

Quick formula: f (Hz) = 1,000 ÷ T (ms)

Example: T = 5 ms → f = 1,000/5 = 200 Hz

10. What is the angular frequency of 60 Hz?

Solution:

  1. Given: f = 60 Hz (US mains frequency)
  2. Formula: ω = 2πf
  3. Calculate: ω = 2π × 60 = 2 × 3.14159 × 60
  4. ω = 376.99 rad/s

Answer: 377 rad/s (rounded) — This angular frequency appears in AC circuit analysis for US power systems.

Frequently Asked Questions

How do you convert Hz to seconds?
To convert frequency (Hz) to period (seconds), use the formula T = 1/f where T is period in seconds and f is frequency in Hz. For example: 50 Hz → T = 1/50 = 0.02 s = 20 ms. First divide 1 by the frequency, then multiply by 1,000 to get milliseconds, or by 1,000,000 to get microseconds.
What is the formula for period from frequency?
The formula for period from frequency is T = 1/f where T is the period (in seconds) and f is the frequency (in Hz). This formula shows that frequency and period are inverse relationships — higher frequency means shorter period, and lower frequency means longer period.
What is the period of 1 Hz?
The period of 1 Hz is exactly 1 second. By definition, 1 Hertz means one cycle per second, so each complete cycle takes 1 second. Formula: T = 1/f = 1/1 = 1 second.
How do you convert seconds to Hz?
To convert period (seconds) to frequency (Hz), use the formula f = 1/T where f is frequency in Hz and T is period in seconds. For example: T = 0.02 s → f = 1/0.02 = 50 Hz. If your period is in milliseconds, first convert to seconds by dividing by 1,000.
What is the period of 100 Hz in milliseconds?
The period of 100 Hz is 10 milliseconds (10 ms). Calculation: T = 1/f = 1/100 = 0.01 seconds = 10 milliseconds. This is a commonly used reference frequency in electronics and testing.
How many hertz are in a second?
Hertz (Hz) and seconds measure different things — they cannot be directly equated. 1 Hz means "one cycle per second" — it's a rate (frequency), not a duration. However, a 1 Hz signal has a period of 1 second, meaning each complete cycle takes 1 second. The relationship is f × T = 1, where f is in Hz and T is in seconds.
What is the difference between frequency and period?
Frequency (f) is the number of cycles per second, measured in Hertz (Hz). Period (T) is the time taken for one complete cycle, measured in seconds. They are mathematical inverses: f = 1/T and T = 1/f. Higher frequency means shorter period, and vice versa. Example: 50 Hz has a period of 0.02 seconds (20 ms).
How do you find angular frequency from Hz?
To find angular frequency (ω) from frequency (f), use the formula ω = 2πf where ω is in radians per second (rad/s) and f is in Hz. For example: f = 50 Hz → ω = 2π × 50 = 314.16 rad/s. Angular frequency is used in physics and engineering for describing oscillations and waves.
What is the period of 50 Hz?
The period of 50 Hz is 0.02 seconds, or 20 milliseconds. Calculation: T = 1/f = 1/50 = 0.02 s = 20 ms. This is the frequency of AC mains electricity in UK, Europe, Australia, and many other countries. Each complete AC cycle takes exactly 20 milliseconds.
How do you convert milliseconds to Hz?
To convert period in milliseconds to frequency in Hz: (1) divide milliseconds by 1,000 to get seconds, (2) take the reciprocal (1 divided by the result). Quick formula: f (Hz) = 1,000 ÷ T (ms). Example: T = 20 ms → f = 1,000/20 = 50 Hz. Or in one step: f = 1/(0.02) = 50 Hz.

Related Calculators

Key Formulas
T = 1 ÷ fPeriod from frequency
f = 1 ÷ TFrequency from period
ω = 2πfAngular frequency
T × f = 1Inverse relationship
Common Frequencies
SourceFrequency
UK Mains50 Hz
US Mains60 Hz
Musical A440 Hz
Audio Ref1 kHz
WiFi 2.4G2.4 GHz
CPU Clock3.6 GHz
Unit Conversions
1 s1,000 ms
1 ms1,000 µs
1 µs1,000 ns
1 ns1,000 ps
1 kHz1,000 Hz
1 MHz106 Hz
1 GHz109 Hz
Quick Tips
  • Higher frequency = shorter period
  • T × f always equals 1
  • 50 Hz → 20 ms period
  • 1 kHz → 1 ms period
  • 1 MHz → 1 µs period

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