Convert Kilohertz to Radians per Second - Frequency Converter

Use this converter to transform frequency given in kilohertz (kHz) into angular frequency expressed in radians per second (rad/s). The conversion is rooted in standard SI definitions and the angular frequency relationship ω = 2π·f.

This tool treats 1 kHz = 1000 Hz exactly and uses the exact mathematical relationship between frequency and angular frequency to deliver high-precision results suitable for engineering, lab work, and documentation.

Guidance is included for choosing significant figures, understanding instrument limits, and ensuring measurement traceability to national standards.

Updated Nov 3, 2025QA PASS — golden 25 / edge 120Run golden-edge-2026-01-23

Governance

Record e5a24283c3aa • Reviewed by Fidamen Standards Committee

Interactive Converter

Convert between kilohertz and radian per second with precision rounding.

Kilohertz (kHz)Radian per Second (rad/s)

Quick reference table

Kilohertz	Radian per Second
KHZ 1.00 kHz	RAD 0.00 rad/s
KHZ 5.00 kHz	RAD 0.00 rad/s
KHZ 10.00 kHz	RAD 0.00 rad/s
KHZ 25.00 kHz	RAD 0.00 rad/s
KHZ 50.00 kHz	RAD 0.0001 rad/s
KHZ 100.00 kHz	RAD 0.0001 rad/s

Methodology

Step 1 — Convert kilohertz to hertz: multiply the kHz value by 1000 because 1 kHz = 1000 Hz (exact in SI).

Step 2 — Compute angular frequency: multiply the frequency in hertz by 2π to obtain ω in rad/s. This follows ω = 2π · f where f is in Hz and π is the mathematical constant.

Precision and reporting: show results with meaningful significant figures based on the input precision and instrument uncertainty. For laboratory or regulatory reporting, state the value and the measurement uncertainty separately and reference traceable calibration certificates.

Key takeaways

Conversion is exact in algorithmic form: multiply kHz by 1000 then by 2π to get rad/s.

For technical and regulatory use, include measurement uncertainty and calibration traceability (for example, reference to NIST or an accredited calibration lab).

Worked examples

Input: 1 kHz → Calculation: ω = 2π × (1 × 1000) = 2000π rad/s → Result ≈ 6283.185307179586 rad/s.

Input: 0.5 kHz → Calculation: ω = 2π × (0.5 × 1000) = 1000π rad/s → Result ≈ 3141.592653589793 rad/s.

Input: 2500 kHz → Calculation: ω = 2π × (2500 × 1000) = 5,000,000π rad/s → Result ≈ 15,707,963.267948966 rad/s.

F.A.Q.

What is the exact mathematical relationship between kHz and rad/s?

Angular frequency ω (in rad/s) is ω = 2π × f, where f is frequency in Hz. Since 1 kHz = 1000 Hz, multiply kHz by 1000 then by 2π (ω = 2π × 1000 × kHz).

Is the radian a base SI unit and how should I report it?

The radian is a derived dimensionless unit used to measure angles in SI. When reporting angular frequency, include the unit 'rad/s' to be explicit that the quantity is angular frequency and not cycles per second.

How many significant digits should I keep?

Match the result precision to the least precise input or to your instrument's measurement uncertainty. For general use, 4–6 significant digits are common; for lab reports use the significant figures supported by your calibrated equipment and include uncertainty.

Are there practical limits or pitfalls when converting very large or small frequencies?

Numerical overflow/underflow can occur for extreme magnitudes in some software environments. In measurement practice, instrument bandwidth, sampling rate, and aliasing limit the usable frequency range. Always verify instrument specifications and use traceable calibration.

How does instrument calibration affect reported values?

Calibration against national standards (traceable to agencies such as NIST or through accredited labs) ensures accuracy. Include calibration dates and uncertainty when using converted values for regulatory or contractual purposes.

When should I use rad/s instead of Hz (or kHz)?

Use rad/s for equations and analyses involving angular motion, rotational dynamics, control systems, and phasor/angular-frequency domains. Use Hz (or kHz) when reporting cycles per second or frequency in common engineering communication contexts.

How do I convert back from rad/s to kHz?

Inverse conversion: f (Hz) = ω / (2π), then kHz = f (Hz) / 1000.

Sources & citations

BIPM — The International System of Units (SI Brochure) — https://www.bipm.org/en/publications/si-brochure
NIST — Metric and SI Units information — https://www.nist.gov/pml/weights-and-measures/si-units
MIT OpenCourseWare — Signals and Systems (background on angular frequency and applications) — https://ocw.mit.edu/courses/6-003-signals-and-systems-fall-2011/
ISO 80000-3:2019 — Space and time — https://www.iso.org/standard/64974.html

Further resources

Related tools

Versioning & Change Control

Audit record (versions, QA runs, reviewer sign-off, and evidence).

Record ID: e5a24283c3aa

What changed (latest)

v1.0.0 • 2025-11-03 • MINOR

Initial publication and governance baseline.

Why: Published with reviewed formulas, unit definitions, and UX controls.

Public QA status

PASS — golden 25 + edge 120

Last run: 2026-01-23 • Run: golden-edge-2026-01-23

Engine

v1.0.0

Data

Baseline (no external datasets)

Content

v1.0.0

Governance

Last updated: Nov 3, 2025

Reviewed by: Fidamen Standards Committee (Review board)

Credentials: Internal QA

Risk level: low

Reviewer profile (entity)

Fidamen Standards Committee

Review board

Internal QA

Entity ID: https://fidamen.com/reviewers/fidamen-standards-committee#person

Semantic versioning

MAJOR: Calculation outputs can change for the same inputs (formula, rounding policy, assumptions).
MINOR: New features or fields that do not change existing outputs for the same inputs.
PATCH: Bug fixes, copy edits, or accessibility changes that do not change intended outputs except for previously incorrect cases.

Review protocol

Verify formulas and unit definitions against primary standards or datasets.
Run golden-case regression suite and edge-case suite.
Record reviewer sign-off with credentials and scope.
Document assumptions, limitations, and jurisdiction applicability.

Assumptions & limitations

Uses exact unit definitions from the Fidamen conversion library.
Internal calculations use double precision; display rounding follows the unit's configured decimal places.
Not a substitute for calibrated instruments in regulated contexts.
Jurisdiction-specific rules may require official guidance.

Change log

v1.0.0 • 2025-11-03 • MINOR

Initial publication and governance baseline.

Why: Published with reviewed formulas, unit definitions, and UX controls.

Areas: engine, content, ui • Reviewer: Fidamen Standards Committee • Entry ID: d0774060fae4