Frequency conversion

Hertz to Radian per Second conversion

Convert frequency in hertz (Hz) to angular frequency in rad/s. Formula, worked examples, and a conversion chart. Switch Hz → rad/s or rad/. Try it free.

Instant result

Result

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Formulas

Core equations used by this converter.

Hz → rad/srad/s = Hz × 6.2831853

Exact factor1 Hz = 6.2831853 rad/s

rad/s → HzHz = rad/s × 0.15915494

iLinear conversion using factor 6.2831853. Prefer the exact factor over rounded multipliers when precision matters.

How to use

Choose Hz → rad/s or rad/s → Hz

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

Enter the value

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

Convert and read the result

Use Convert or let the result update automatically.

Example conversions

Common values with formula and result.

1 Hz to rad/s

1 × 2π ≈ 6.283185307 rad/s

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

50 × 2π ≈ 314.159265 rad/s

60 Hz to rad/s

60 × 2π ≈ 376.991118 rad/s

440 Hz to rad/s (A4)

440 × 2π ≈ 2764.60154 rad/s

Hertz to Radian per Second conversion specification

Version 1.1.0 · Engine tested

Calculation status

Engine tested 4 published cases
Named expert review Not performed
Calculation version 1.1.0

Review policy

Definition: Hertz (Hz) converts to rad/s using a fixed linear factor. Convert frequency in hertz (Hz) to angular frequency in rad/s. Exact: ω = 2πf. Formula, worked examples, and a conversion chart.
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: rad/s = Hz × 6.2831853 · 1 Hz = 6.2831853 rad/s
Hertz to rad/s conversion table: Hertz (Hz) rad/s (≈)
0.159155 Hz 1 rad/s
1 Hz 6.283185 rad/s
10 Hz 62.83185 rad/s
50 Hz 314.1593 rad/s
60 Hz 376.9911 rad/s
100 Hz 628.3185 rad/s
440 Hz 2764.602 rad/s
1000 Hz 6283.185 rad/s
Assumptions: Conversion runs locally in the browser; values are not uploaded.
Uses the standard factor/definition for these units.
Units: Hz → rad/s
rad/s → Hz
Boundary conditions: Empty or non-numeric input yields no valid result.
Non-negative values are expected for physical quantities.
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: SI / international unit definitions where applicable
CalculatorX conversion factors (local runtime)
Calculation version: 1.1.0

Hertz (Hz)	rad/s (≈)
0.159155 Hz	1 rad/s
1 Hz	6.283185 rad/s
10 Hz	62.83185 rad/s
50 Hz	314.1593 rad/s
60 Hz	376.9911 rad/s
100 Hz	628.3185 rad/s
440 Hz	2764.602 rad/s
1000 Hz	6283.185 rad/s

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.

Frequently asked questions

Key distinctions behind the conversion.

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

Use 1 Hz = 6.283185307179586 rad/s. 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.