Réaumur to Rankine Converter - Convert °Ré to °R
Convert precisely with °R = (°Ré × 9/4) + 491.67. The reverse identity is °Ré = (°R − 491.67) × 4/9. Very small or large outputs switch to scientific notation automatically for clarity.
Exact identity: °R = (°Ré × 9/4) + 491.67. See all online temperature unit converters.
About Réaumur to Rankine Conversion
Réaumur (°Ré) is a historical interval scale that sets 0 °Ré at the freezing point of water and 80 °Ré at boiling, dividing the freezing–boiling span into 80 equal steps. Rankine (°R) is an absolute temperature scale that uses the Fahrenheit-sized degree: absolute zero is 0 °R, and 1 °R equals 1 °F of increment. While Kelvin (K) is the SI base unit of thermodynamic temperature, Rankine remains common in certain U.S.-centric engineering contexts where Fahrenheit-based increments are preferred. Converting °Ré to °R therefore bridges a historical interval scale and a modern absolute scale with a precise linear mapping.
The transformation is built from exact identities. Since °Ré and °C share the same zero at freezing, the interval mapping is a simple scale: °C = °Ré × 5/4. Next, Celsius to Fahrenheit applies a ratio and an offset: °F = (°C × 9/5) + 32. Finally, Rankine is the absolute version of Fahrenheit: °R = °F + 459.67. Collapsing the chain yields °R = (°Ré × 9/4) + 491.67, where 491.67 °R is the Rankine temperature at 0 °C (i.e., 273.15 K × 9/5). The result is exact within the conventional constants and perfectly suitable for documentation, audit trails, and calibration narratives.
Réaumur to Rankine Formula
Exact relationship
°R = (°Ré × 9/4) + 491.67
// inverse
°Ré = (°R − 491.67) × 4/9Dimensional/interval breakdown:
°C = °Ré × 5/4 (exact)
°F = (°C × 9/5) + 32 (exact)
°R = °F + 459.67 (exact)
⇒ °R = (°Ré × 9/4) + 491.67 (exact)Related Temperature Converters
What is Réaumur (°Ré)?
Réaumur divides the 0–100 °C interval into 80 equal parts, sharing the same zero as Celsius at the freezing point of water. Because the zeros coincide, °Ré ↔ °C is a pure scale transformation needing no offset: °C = °Ré × 5/4 and °Ré = °C × 4/5. Although modern instruments rarely use °Ré, it still appears in historical literature, museum instrumentation, and educational materials discussing the evolution of temperature scales.
In modern pipelines, you will typically convert °Ré to an SI-consistent representation (°C or K) for storage and computation, then present other scales as needed.
What is Rankine (°R)?
Rankine is an absolute scale analogous to Kelvin but uses Fahrenheit-sized degrees. Absolute zero is 0 °R, and the exact bridge to Kelvin is °R = K × 9/5. This makes Rankine convenient in calculations that otherwise operate with Fahrenheit-based increments. Because Rankine is absolute, conversions to or from interval scales like °Ré require both a degree-size rescaling and an absolute offset adjustment, which the compact formula above encapsulates.
Example anchors: 0 °C equals 491.67 °R, and 100 °C equals 671.67 °R-useful landmarks when sanity-checking computations.
Step-by-Step: Converting °Ré to °R
- Start with a temperature in Réaumur (°Ré).
- Compute °C = °Ré × 5/4 to recover the Celsius interval value.
- Compute °F = (°C × 9/5) + 32 to express the temperature on the Fahrenheit interval.
- Compute °R = °F + 459.67 to obtain the absolute Rankine temperature.
- Round once at presentation and retain full internal precision to avoid cumulative rounding in chained conversions.
Example walkthrough:
Input: 16.0 °Ré
Compute: °C = 16.0 × 5/4 = 20.0
°F = 20.0 × 9/5 + 32 = 68.0
°R = 68.0 + 459.67 = 527.67
Output: 527.67 °R (UI rounding only)Common Conversions
| Réaumur (°Ré) | Rankine (°R) |
|---|---|
| -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 |
Quick Reference Table (Reverse)
| Rankine (°R) | Réaumur (°Ré) |
|---|---|
| 0.00 | -218.520000 |
| 419.67 | -32.000000 |
| 491.67 | 0.000000 |
| 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 |
Precision, Rounding & Significant Figures
Operational rounding
Compute the chain with full precision (°Ré→°C→°F→°R) and round once at display or export. Declare your rounding policy (e.g., “°R to one or two decimals unless otherwise specified”) and keep unrounded values in storage to eliminate drift in pipelines and reports.
Consistent documentation
Keep the identities clearly visible near examples (°R = (°Ré × 9/4) + 491.67 and °Ré = (°R − 491.67) × 4/9). Use explicit symbols (°Ré, °C, °F, °R) in headings, legends, and column names to avoid ambiguity.
Where This Converter Is Used
- Integrating historical °Ré records with absolute-temperature analyses conducted in Rankine or Kelvin.
- Education and training materials that contrast interval scales (°Ré/°C/°F) with absolute scales (°R/K).
- Museum and restoration labeling that presents legacy °Ré alongside absolute temperatures for modern audiences.
- Engineering workflows that prefer Fahrenheit increments but demand absolute baselining for thermodynamic calculations.
Frequently Asked Questions
What is the exact formula to convert Réaumur to Rankine?
Use °R = (°Ré × 9/4) + 491.67. First convert °Ré to °C with ×5/4, then to °F with ×9/5 and +32, and finally to °R by adding 459.67. Combining the steps yields +491.67 and a net scale of 9/4.
How do I convert back from Rankine to Réaumur?
Use °Ré = (°R − 491.67) × 4/9. Subtract 491.67 to remove the absolute offset and scale by 4/9 to express the result on the Réaumur interval.
Where do the constants 491.67 and 9/4 come from?
491.67 °R equals 273.15 K × 9/5-the Rankine value at 0 °C. The factor 9/4 comes from (5/4)×(9/5) after converting °Ré→°C (×5/4) and °C→°F (×9/5); the 5 cancels, leaving 9/4.
Is the conversion exact or approximate?
Within the conventional constants (273.15 K for 0 °C and 459.67 for the °F→°R offset), the mapping is exact and linear. No curve fits or empirical corrections are used.
Do negative or fractional Réaumur inputs convert correctly?
Yes. The mapping is linear and sign-preserving after adjusting the absolute offset. Fractional and negative values convert without ambiguity.
How is Rankine related to Kelvin?
Rankine uses the Fahrenheit degree size with an absolute zero at 0 °R. The exact identity is °R = K × 9/5 and, conversely, K = °R × 5/9.
What anchor pairs help with quick checks?
0 °Ré → 491.67 °R; 20 °Ré → 536.67 °R; 29.6 °Ré → 558.27 °R; 80 °Ré → 671.67 °R; −32 °Ré → 419.67 °R.
How should I round results for reports and dashboards?
Keep full internal precision and round once at presentation. Rankine values are often shown to one or two decimals in summaries; use more when your application demands it.
Does locale formatting affect the computation?
No. Localization changes only number appearance (decimal symbol and digit grouping). The arithmetic uses the same constants regardless of locale.
How does this relate to Celsius and Fahrenheit?
The chain is °Ré → °C via ×5/4, °C → °F via ×9/5 and +32, and °F → °R via +459.67. Collapsing those steps yields the compact form °R = (°Ré × 9/4) + 491.67.
Any mental math tips for °Ré → °R?
Multiply °Ré by 2.25 (that’s 9/4) and add 491.67. Example: 16 °Ré → 16×2.25 = 36; 36 + 491.67 = 527.67 °R.
What symbols should I keep consistent?
Use °Ré for Réaumur and °R for Rankine. Kelvin uses K without a degree symbol.
Tips for Working with °Ré, °C, °F & °R
- Memorize anchors: 0 °Ré ↔ 491.67 °R; 20 °Ré ↔ 536.67 °R; 80 °Ré ↔ 671.67 °R.
- Round once at presentation; centralize rounding policy in the reporting layer.
- Prefer canonical storage in Kelvin; generate interval/absolute displays (°Ré/°F/°R) late in the pipeline.
- For quick validation, compute both directions and confirm round-trip within your rounding threshold.