Rankine to Réaumur Converter - Convert °R to °Ré
Convert precisely with °Ré = (°R − 491.67) × 4/9. The reverse identity is °R = (°Ré × 9/4) + 491.67. Very small or large outputs switch to scientific notation automatically for clarity.
Exact identity: °Ré = (°R − 491.67) × 4/9. See all temperature conversion calculators.
About Rankine to Réaumur Conversion
Rankine (°R) is an absolute temperature scale built on the Fahrenheit degree size: 0 °R is absolute zero and 1 °R equals 1 °F of interval. Réaumur (°Ré) is a historical interval scale aligned with the freezing point of water at 0 °Ré and the boiling point at 80 °Ré. Converting °R to °Ré therefore involves removing the absolute offset to reach a familiar water-fixed interval and then resizing the degree to match Réaumur.
The exact, auditable path is °R → °F by subtracting 459.67 (since °R = °F + 459.67), °F → °C via (°F − 32) × 5/9, and °C → °Ré through ×4/5. Collapsing yields the compact closed form: °Ré = (°R − 491.67) × 4/9. This identity is linear, uses conventional constants (273.15 K ↔ 0 °C; 459.67 °R offset), and introduces no empirical approximations.
Rankine to Réaumur Formula
Exact relationship
°Ré = (°R − 491.67) × 4/9
// inverse
°R = (°Ré × 9/4) + 491.67Dimensional/interval breakdown:
°F = °R − 459.67 (exact)
°C = (°F − 32) × 5/9 (exact)
°Ré = °C × 4/5 (exact)
⇒ °Ré = (°R − 491.67) × 4/9 (exact)Related Temperature Converters
What is Rankine (°R)?
Rankine mirrors Kelvin conceptually but uses Fahrenheit-sized degrees. Absolute zero is 0 °R, and the conversion to Kelvin is exactly K = °R × 5/9. This makes Rankine useful for thermodynamic calculations in U.S.-customary contexts where Fahrenheit is standard. However, because Rankine is absolute while Réaumur is an interval scale, you must adjust both offset and degree size when moving between them.
Familiar anchors: 0 °C equals 491.67 °R, 100 °C equals 671.67 °R-handy checks when reconstructing or auditing pipelines.
What is Réaumur (°Ré)?
Réaumur sets 0 °Ré at the freezing point of water and 80 °Ré at boiling, making a pure ratio to Celsius: °Ré = °C × 4/5 and °C = °Ré × 5/4. Although rarely used in modern instrumentation, it remains important in historical literature and pedagogy about temperature scales. Because Réaumur shares the freezing zero with Celsius, transitions between °Ré and °C are offset-free.
In contemporary practice, you will often normalize to Kelvin or Celsius for computation and database storage, generating °Ré for historical alignment or teaching materials.
Step-by-Step: Converting °R to °Ré
- Start with a temperature in Rankine (°R).
- Remove the absolute offset: compute °R − 491.67 to reach a value relative to 0 °C.
- Scale by 4/9 to resize the degree from Fahrenheit-sized increments to the Réaumur interval.
- Round once at presentation and store high-precision values internally for clean chained conversions.
Example walkthrough:
Input: 527.67 °R
Compute: °Ré = (527.67 − 491.67) × 4/9 = 36 × 4/9 = 16.0
Output: 16.0 °Ré (UI rounding only)Common Conversions
| Rankine (°R) | Réaumur (°Ré) |
|---|---|
| 0.00 | -218.520000 |
| 419.67 | -32.000000 |
| 491.67 | 0.000000 |
| 509.67 | 8.000000 |
| 527.67 | 16.000000 |
| 536.67 | 20.000000 |
| 558.27 | 29.600000 |
| 581.67 | 40.000000 |
| 627.67 | 64.000000 |
| 645.67 | 72.000000 |
| 671.67 | 80.000000 |
| 716.67 | 100.000000 |
Quick Reference Table (Reverse)
| Réaumur (°Ré) | Rankine (°R) |
|---|---|
| -218.520000 | 0.00 |
| -32.000000 | 419.67 |
| 0.000000 | 491.67 |
| 8.000000 | 509.67 |
| 16.000000 | 527.67 |
| 20.000000 | 536.67 |
| 29.600000 | 558.27 |
| 40.000000 | 581.67 |
| 64.000000 | 627.67 |
| 72.000000 | 645.67 |
| 80.000000 | 671.67 |
| 100.000000 | 716.67 |
Precision, Rounding & Significant Figures
Operational rounding
Perform °R→°F→°C→°Ré with full precision and round once at the final display. Publish a clear rounding standard (e.g., “°Ré to two decimals by default”) and retain unrounded values in storage for reproducibility and reliable round-trip checks.
Consistent documentation
Keep the identities near worked examples (°Ré = (°R − 491.67) × 4/9 and °R = (°Ré × 9/4) + 491.67). Use explicit symbols (°R, °F, °C, °Ré) in headings, legends, and export column names.
Where This Converter Is Used
- Reconciling absolute-temperature datasets (°R/K) with historical interval records in °Ré.
- Educational materials contrasting absolute and interval scales with exact linear transformations.
- Museum/restoration contexts presenting legacy °Ré readings alongside absolute-scale equivalents.
- Engineering documentation that needs Fahrenheit-based absolute temperatures yet references historical sources.
Frequently Asked Questions
What is the exact formula to convert Rankine to Réaumur?
Use °Ré = (°R − 491.67) × 4/9. Subtract 491.67 to remove the absolute Rankine offset (0 °C = 491.67 °R) and scale the degree size by 4/9 to reach Réaumur.
How do I convert back from Réaumur to Rankine?
Use °R = (°Ré × 9/4) + 491.67. It inverts the scaling and restores the absolute offset.
Why 491.67 and 4/9?
491.67 °R equals 0 °C in Rankine (273.15 K × 9/5). The scale factor 4/9 comes from the inverse of 9/4 used in °Ré → °R, reflecting the relation among °Ré, °C, and °F degree sizes.
Is Rankine absolute and Réaumur interval?
Yes. Rankine is absolute (0 °R at absolute zero) with Fahrenheit-sized degrees. Réaumur is an interval scale sharing its zero with °C at the freezing point of water.
Is the conversion exact or approximate?
Within the conventional constants (273.15 K ↔ 0 °C; 459.67 °R offset to °F), it is exact and linear.
Do large or negative Rankine values convert correctly?
Yes. The function is linear. After removing the offset, the rescaling by 4/9 handles any magnitude while preserving sign.
What anchor pairs help with quick checks?
491.67 °R → 0 °Ré; 536.67 °R → 20 °Ré; 558.27 °R → 29.6 °Ré; 671.67 °R → 80 °Ré; 419.67 °R → −32 °Ré.
How should I round results for reports?
Round once at presentation. Two to three decimals are often adequate for °Ré; use more precision when calibrated instrumentation justifies it.
Does locale formatting affect the computation?
No. It changes only number appearance, not the underlying arithmetic.
How does this relate to Kelvin and Celsius?
You can equivalently compute °Ré from K: °Ré = (K − 273.15) × 4/5 with K = °R × 5/9. Substituting yields the same compact identity (°R − 491.67) × 4/9.
Any mental math tips for °R → °Ré?
Subtract 491.67, then multiply by about 0.444… (that’s 4/9). Example: 527.67 °R → (36) × 4/9 = 16 °Ré.
What symbols should I keep consistent?
Use °R for Rankine and °Ré for Réaumur. Kelvin uses K without a degree symbol.
Tips for Working with °R, K, °C & °Ré
- Memorize anchors: 491.67 °R ↔ 0 °Ré; 536.67 °R ↔ 20 °Ré; 671.67 °R ↔ 80 °Ré.
- Round once at presentation; keep Kelvin as the canonical storage when possible (K = °R × 5/9).
- Document constants (273.15, 459.67, 9/5, 5/9, 4/5) and the stepwise chain for audits and peer review.
- Validate with reverse calculations and confirm round-trip within your rounding policy.