HomeCalculatorsPhysicsHz to Rad/s Converter
Physics calculator

Hz to Rad/s Converter

Convert between hertz and radians per second with ω = 2πf. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 2/2 declared partitions (hz-rads, invalid-domain) · Matrix
Known limitations
  • Angular frequency
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Hz ↔ rad/s conversion.
Scope
SI radian
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity
1/1 property · digest fa8f737b6f69
Legacy regression
3/3 tests · Production surface contract 4/4
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review
Internal · Pass
Named expert review
Not performed
CVP suite
1/1 golden · 1/1 CVP boundary · 1/1 invalid · 1/1 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources
  • SI derived units — radian / hertz
  • NIST / SI frequency — hertz and radian per second
Sources
Evidence
1 legacy golden · 1 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 1/1 invalid · Artifact integrity PASS · CalculatorX physics/RF review
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Hz → rad/sω = 2πf
rad/s → Hzf = ω/(2π)
iUses SI radian measure (not degrees/s).

How to use

1

Choose Hz → rad/s or rad/s → Hz

Angular frequency ω = 2πf.

2

Enter the value

Frequency must be greater than zero.

3

Read the converted result

f = ω / (2π) in the reverse direction.

Example calculations

Common configurations with formula and result.

ϟ

1 Hz

one cycle per second

2π·1
6.283185… rad/s

Hz to Rad/s converter specification

Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-09

Calculation status

Review policy · Evidence · Reviewed by CalculatorX physics/RF review

Definition
Angular frequency: ω = 2πf and f = ω/(2π). Frequency must be > 0.
What it calculates
Hz ↔ rad/s conversion.
Inputs
  • mode hz-rad|rad-hz
  • value
Outputs
  • ω or f number
Formula
ω=2πf
Assumptions
  • SI radian
Units
  • Hz, rad/s
Boundary conditions
  • value≤0 → VALUE_MUST_BE_POSITIVE
Example
1 Hz → 2π rad/s
Validation cases

1 published on this page · 3/3 tests · Production surface contract 4/4 · View evidence

  • hz-rad value=1 → 6.283185307179586
Sources
  • SI derived units — radian / hertz
    Supports: ω = 2πf
  • NIST / SI frequency — hertz and radian per second
    Supports: ω = 2πf
Last reviewed
2026-08-09
Reviewed by
CalculatorX physics/RF review
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Convert Hz ↔ rad/s with Trusted Template guards.

Supported and not supported

Supported — Bidirectional Hz↔rad/s · API units.frequency.hz_rads

Not supported — deg/s, rpm, degree-based phase

Agent / API notes

Capability id: units.frequency.hz_rads · tool id: hz-rads · pin 1.0.0.

Other calculators in this family: Wavelength, LC Match .

λ Wavelength › LC LC Match ›
}

Frequently asked questions

Key distinctions behind the calculation.

Can frequency be zero or negative?

No. The API returns VALUE_MUST_BE_POSITIVE for non-positive values.