HomeConvertersFrequencyHertz to Radian per Second conversion
Frequency conversion

Hertz to Radian per Second conversion

Convert frequency in hertz (Hz) to angular frequency in rad/s. Use the exact 2π relation in either direction and see worked examples.

Instant result
Result
—

Enter values to convert.

Inputs —
Mode —
Formula —

Formulas

Core equations used by this converter.

Hz → rad/sω = 2πf
Exact definition1 cycle = 1 turn = 2π rad
rad/s → Hzf = ω ÷ (2π)
iThe two rates use the same one-second time base. The factor 2π is exact and displayed results may be rounded.

How to use

1

Choose Hz → rad/s or rad/s → Hz

Use the tabs to switch direction. Forward mode needs hertz; reverse uses the opposite unit.

2

Enter the value

Type a non-negative value in the active unit field.

3

Convert and read the result

Use Convert or let the result update automatically.

Example conversions

Common values with formula and result.

ϟ

1 Hz to rad/s

1 Hz to rad/s

1 × 2π ≈ 6.283185307 rad/s
1 × 2π ≈ 6.283185307 rad/s
ϟ

50 Hz to rad/s (mains frequency, many regions)

50 Hz to rad/s (mains frequency, many regions)

50 × 2π ≈ 314.159265 rad/s
50 × 2π ≈ 314.159265 rad/s
ϟ

60 Hz to rad/s

60 Hz to rad/s

60 × 2π ≈ 376.991118 rad/s
60 × 2π ≈ 376.991118 rad/s
ϟ

440 Hz to rad/s (A4)

440 Hz to rad/s (A4)

440 × 2π ≈ 2764.60154 rad/s
440 × 2π ≈ 2764.60154 rad/s

Hertz to Radian per Second conversion specification

Version 1.1.1 · Engine tested

Calculation status
  • Engine tested 4 published cases
  • Named expert review Not performed
  • Calculation version 1.1.1

Review policy

Definition
One full cycle corresponds to one turn, or 2π radians. The calculator relates cyclic frequency in Hz to angular frequency in rad/s for the same periodic motion.
What it calculates
Value between Hz and rad/s. Switch direction with the converter tabs.
Inputs
  • Hertz (Hz) or reverse unit (rad/s)
Outputs
  • Converted value in rad/s or Hz
Formula
ω = 2πf · f = ω ÷ (2π)
Hertz to rad/s conversion table
Hertz (Hz)rad/s (≈)
0.159155 Hz1 rad/s
1 Hz6.283185 rad/s
10 Hz62.83185 rad/s
50 Hz314.1593 rad/s
60 Hz376.9911 rad/s
100 Hz628.3185 rad/s
440 Hz2764.602 rad/s
1000 Hz6283.185 rad/s
Assumptions
  • Conversion runs locally in the browser; values are not uploaded.
  • Each cycle corresponds to one full turn of phase.
Units
  • Hz → rad/s
  • rad/s → Hz
Boundary conditions
  • Empty or non-numeric input yields no valid result.
  • Frequency magnitudes must be nonnegative.
Example
1 Hz → 6.28319 rad/s
Validation cases
  • 1 Hz → 6.2831853 rad/s
  • 10 Hz → 62.831853 rad/s
  • 50 Hz → 314.15927 rad/s
  • 100 Hz → 628.31853 rad/s
Sources
  • NIST SP 330, Section 2 (https://www.nist.gov/pml/special-publication-330/sp-330-section-2)
  • CalculatorX UUCE turn and radian definitions, snapshot 0.3.0-preview.3
Calculation version
1.1.1

Background

Interpretation and common distinctions.

Use the converter tabs to switch direction when available. Results for Hertz to Radian per Second conversion update locally in your browser.

hz Radian/sec to hertz › hz Hertz to kilohertz › hz Hertz to megahertz ›

Frequently asked questions

Key distinctions behind the conversion.

How do you convert using Hertz to Radian per Second conversion?

Multiply the cyclic rate by 2π. Example: 1 Hz to rad/s → 1 × 2π ≈ 6.283185307 rad/s.

Can I switch direction?

Use the converter tabs when available, or open the related reverse tool from Related.

Does this run online or locally?

Calculation runs locally in your browser. Values are not uploaded.

How precise are the results?

Results follow the formulas on this page. Round to the precision your use case needs.