Thermal Expansion Converter
Print pageAll Equivalents Reference Table
| Unit | Equivalent Value |
|---|
The Coefficient of Linear Thermal Expansion (symbolized by α) quantifies the fractional change in a material’s length per unit change in temperature (α = (1 ÷ L0) · (dL ÷ dT)), allowing engineers to compute dimensional growth (ΔL = α · L0 · ΔT). Similarly, the Coefficient of Volumetric Thermal Expansion (β) measures fractional volume change (ΔV = β · V0 · ΔT, where for isotropic solids β ≈ 3 · α). Across bridge expansion joint design, reinforced concrete rebar bonding, aerospace airframe riveting, precision optical telescope mirrors, and piping thermal stress analysis, thermal expansion coefficients are categorized across five global units: 1/Kelvin (1/K), 1/Degree Celsius (1/°C), 1/Degree Fahrenheit (1/°F), 1/Degree Rankine (1/°R), and 1/Degree Réaumur (1/°r).
Our free online Thermal Expansion Converter provides instant, high-precision conversions across all SI metric, Imperial engineering, and materials science thermal expansion coefficient units:
- 1/Degree Celsius to 1/Degree Fahrenheit (1/°C to 1/°F): Multiply 1/°C by
0.55555556(5/9) (A material CTE of 11.7 × 10-6 /°C = 6.5 × 10-6 /°F). - 1/Degree Fahrenheit to 1/Degree Celsius (1/°F to 1/°C): Multiply 1/°F by
1.8(A material CTE of 6.5 × 10-6 /°F = 11.7 × 10-6 /°C). - 1/Kelvin to 1/Degree Celsius (1/K to 1/°C):
1/K = 1/°C(1:1 identical magnitude). - 1/Degree Rankine to 1/Degree Fahrenheit (1/°R to 1/°F):
1/°R = 1/°F(1:1 identical magnitude). - 1/Degree Réaumur to 1/Kelvin (1/°r to 1/K): Multiply 1/°r by
1.25(1/°r = 1.25 /°C = 1.25 /K = 0.6944 /°F).
Master Coefficient of Thermal Expansion (CTE) Conversion Table
The table below displays exact mathematical conversion relationships, SI 1/K multipliers, and imperial 1/°F equivalents relative to 1 per Kelvin (1/K = 1/°C):
| Thermal Expansion Unit Name | Symbol | Exact Value in 1/K (1/°C) | 1/°F & 1/°R Equivalent | Domain & Technical Application Standard |
|---|---|---|---|---|
| 1 per Kelvin | 1/K, K-1 |
1.0 /K (Base SI Unit) |
0.555556 /°F (0.555556 /°R / 1.0 /°C) |
SI Fundamental Thermal Expansion Standard |
| 1 per Degree Celsius | 1/°C, °C-1 |
1.0 /°C |
0.555556 /°F (0.555556 /°R / 0.8 /°r) |
Global Metric Materials Science CTE Standard |
| 1 per Degree Fahrenheit | 1/°F, °F-1 |
1.8 /K (1.8 /°C) |
1.0 /°F (1.0 /°R / 1.44 /°r) |
US Customary Civil Engineering & HVAC Standard |
| 1 per Degree Rankine | 1/°R, °R-1 |
1.8 /K (1.8 /°C) |
1.0 /°F (1.0 /°R) |
US Aerospace & High-Temperature Engineering |
| 1 per Degree Réaumur | 1/°r, °r-1 |
0.8 /K (0.8 /°C) |
0.444444 /°F (0.444444 /°R) | Historical European Scientific Material CTE |
Step-by-Step Structural Expansion Calculation Example
To convert structural carbon steel with a Coefficient of Thermal Expansion of 11.7 × 10-6 per Degree Celsius (11.7 μm/m/°C) into Imperial 1/°F and calculate expansion (ΔL) for a 100-meter beam across a Δ50°C (Δ90°F) temperature change:
Step 1 (Imperial 1/°F Unit): α = 11.7 × 10-6 × (5 ÷ 9) = 6.5 × 10-6 /°F
Step 2 (Metric Beam Expansion): ΔL = (11.7 × 10-6) × 100 m × 50°C = 0.0585 m (58.5 mm)
Step 3 (Imperial Beam Expansion Verification): ΔL = (6.5 × 10-6) × 328.084 ft × 90°F = 0.1919 ft (2.30 inches)
Thus, structural steel (11.7 × 10-6 /°C) equals 6.5 × 10-6 /°F, causing a 100m bridge girder to expand by 58.5 mm (2.30 inches) over a Δ50°C summer-winter temperature span.
Real-World Engineering Material Thermal Expansion Benchmarks
Below is a comparative reference chart showing linear thermal expansion coefficients (α) across Invar alloy, glass, structural steel, concrete, and aluminum:
| Solid Material / Structural Element | Linear CTE in Metric (α in 10-6 /°C) | Linear CTE in Imperial (α in 10-6 /°F) | Engineering & Physical Application Context |
|---|---|---|---|
| Invar (36% Ni Fe-Ni Alloy FeNi36) | 1.2 × 10-6 /°C | 0.67 × 10-6 /°F | Ultra-low expansion for precision optical mounts & pendulum clocks |
| Pyrex Borosilicate Glass | 3.3 × 10-6 /°C | 1.83 × 10-6 /°F | Thermal shock resistant cookware & laboratory glassware |
| Structural Concrete (Aggregate Matrix) | 10.0 – 12.0 × 10-6 /°C | 5.5 – 6.7 × 10-6 /°F | Civil infrastructure (near-perfect CTE match with steel rebar!) |
| Carbon Structural Steel / Rebar | 11.7 × 10-6 /°C | 6.50 × 10-6 /°F | Standard reinforced concrete rebar & bridge I-beams |
| Copper / Architectural Brass | 16.5 – 18.5 × 10-6 /°C | 9.17 – 10.28 × 10-6 /°F | Electrical busbars, plumbing pipes & bimetallic thermostats |
| Structural Aluminum Alloys (6061-T6) | 23.0 × 10-6 /°C | 12.78 × 10-6 /°F | High thermal expansion (twice structural steel rate) |
History & Physics: 1896 Guillaume Invar Discovery (Nobel Prize) vs Bimetallic Differential Expansion
1896 Charles Édouard Guillaume & the Invention of Invar (1920 Nobel Prize)
In 1896, Swiss physicist Charles Édouard Guillaume discovered that an alloy of 36% nickel and 64% iron (termed Invar, short for invariable) exhibits a near-zero Coefficient of Thermal Expansion (α ≈ 1.2 × 10-6 /°C). Guillaume’s breakthrough revolutionized geodetic land surveying baseline tapes, chronometer pendulum balance springs, and optical mirror frames. For his discovery of low-expansion nickel-steel alloys, Guillaume was awarded the 1920 Nobel Prize in Physics.
Bimetallic Strip Thermostats & Differential Expansion
Mechanical thermostats, circuit breakers, and thermal overload relays utilize bimetallic strips created by bonding two metals with contrasting CTEs—typically brass (α ≈ 19 × 10-6 /°C) and steel (α ≈ 11.7 × 10-6 /°C). Upon heating, brass expands faster than steel, forcing the bonded strip to bend predictably toward the steel side to open electrical contacts or actuate mechanical valves.
Popular direct tools:
Frequently Asked Questions (FAQ)
How do you convert 1/°C to 1/°F for Thermal Expansion?
To convert a Coefficient of Thermal Expansion from 1/°C to 1/°F, multiply the 1/°C value by 5/9 (0.55555556). For example, steel’s CTE of 11.7 × 10-6 /°C × (5 ÷ 9) = 6.5 × 10-6 /°F.
How do you convert 1/°F to 1/°C for Thermal Expansion?
To convert a Coefficient of Thermal Expansion from 1/°F to 1/°C, multiply the 1/°F value by 1.8. For example, 6.5 × 10-6 /°F × 1.8 = 11.7 × 10-6 /°C.
Why do concrete and steel rebar have nearly identical thermal expansion?
Structural steel (11.7 × 10-6 /°C) and concrete (10 to 12 × 10-6 /°C) share almost identical CTE values. This natural physical match prevents reinforced concrete structures from cracking or debonding during summer-winter thermal cycles.
What is the relationship between Linear (α) and Volumetric (β) Thermal Expansion?
For isotropic solid materials (which expand equally in all 3 spatial directions), the Volumetric Thermal Expansion Coefficient (β) is approximately three times the Linear Thermal Expansion Coefficient: β ≈ 3 · α.