Calories (thermochemical)/gram celsius to Joules/kilogram kelvin Converter (cal/(g·°C) to J/(kg·K))

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1 Calorie/gram celsius = 4184.00000241 Joule/kilogram kelvin

1 cal/(g·°C) = 4184.000002 J/(kg·K) • 1 J/(kg·K) = 0.000239006 cal/(g·°C)

Decimals:

Certified Authority Value

4184.00000241

J/(kg·K)

From / Input

cal/(g·°C)

Swap to Joule/kilogram kelvin to Calorie/gram celsius

To / Result

J/(kg·K)

Quick Values:

Conversion Formula

To convert Calorie/gram celsius to Joule/kilogram kelvin, multiply by 4184.00000241

cal/(g·°C) × 4184.00000241 = J/(kg·K)

Calculation: 1 cal/(g·°C) × 4184.00000241 = 4184.00000241 J/(kg·K)

Common Calorie/gram celsius to Joule/kilogram kelvin Calculations

Quick-lookup reference table showing calculated equivalents for standard increments between Calorie/gram celsius (cal/(g·°C)) and Joule/kilogram kelvin (J/(kg·K)).

Tap any row to calculate

Calorie/gram celsius to Joule/kilogram kelvin: Primary Direct Table (15 Steps)

Rule: 1 Calorie/gram celsius is equal to 4184.000002 J/(kg·K) (Joule/kilogram kelvin)

Calorie/gram celsius to Joule/kilogram kelvin Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 cal/(g·°C) 4.184 J/(kg·K)	4.184 × 10⁰
0.01 cal/(g·°C) 41.84 J/(kg·K)	4.184 × 10¹
0.1 cal/(g·°C) 418.4 J/(kg·K)	4.184 × 10²
0.5 cal/(g·°C) 2092.000001 J/(kg·K)	2.092 × 10³
1 cal/(g·°C) 4184.000002 J/(kg·K)	4.184 × 10³
2 cal/(g·°C) 8368.000005 J/(kg·K)	8.368 × 10³
5 cal/(g·°C) 20920.000012 J/(kg·K)	2.092 × 10⁴
10 cal/(g·°C) 41840.000024 J/(kg·K)	4.184 × 10⁴
20 cal/(g·°C) 83680.000048 J/(kg·K)	8.368 × 10⁴
25 cal/(g·°C) 104600.00006 J/(kg·K)	1.046 × 10⁵
50 cal/(g·°C) 209200.00012 J/(kg·K)	2.092 × 10⁵
100 cal/(g·°C) 418400.000241 J/(kg·K)	4.184 × 10⁵
250 cal/(g·°C) 1046000.000602 J/(kg·K)	1.046 × 10⁶
500 cal/(g·°C) 2092000.001205 J/(kg·K)	2.092 × 10⁶
1000 cal/(g·°C) 4184000.00241 J/(kg·K)	4.184 × 10⁶

Joule/kilogram kelvin to Calorie/gram celsius: Reciprocal Summary

Rule: 1 Joule/kilogram kelvin is equal to 0.000239006 cal/(g·°C) (Calorie/gram celsius)

Joule/kilogram kelvin to Calorie/gram celsius Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 J/(kg·K) 0.000239006 cal/(g·°C)	2.39 × 10⁻⁴
5 J/(kg·K) 0.00119503 cal/(g·°C)	1.195 × 10⁻³
10 J/(kg·K) 0.00239006 cal/(g·°C)	2.39 × 10⁻³
50 J/(kg·K) 0.0119503 cal/(g·°C)	1.195 × 10⁻²
100 J/(kg·K) 0.0239006 cal/(g·°C)	2.39 × 10⁻²

View Complete 15-Row Joule/kilogram kelvin to Calorie/gram celsius Table

Real-World Context & Everyday Benchmarks

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To help contextualize these units in everyday life, science, and engineering, here are verified real-world reference points for Calorie/gram celsius (cal/(g·°C)) and Joule/kilogram kelvin (J/(kg·K)):

Calorie/gram celsius References:

Pure liquid water standard specific heat capacity at 25°C 1 cal/(g·°C)
Dry atmospheric air specific heat at constant pressure cp 0.240201 cal/(g·°C)
Solid structural aluminum metal specific heat capacity 0.214388 cal/(g·°C)
Pure electrical copper metal specific heat capacity 0.092017 cal/(g·°C)

Joule/kilogram kelvin References:

Pure liquid water standard specific heat capacity at 25°C 4184 J/(kg·K)
Dry atmospheric air specific heat at constant pressure cp 1005 J/(kg·K)
Solid structural aluminum metal specific heat capacity 897 J/(kg·K)
Pure electrical copper metal specific heat capacity 385 J/(kg·K)
Dense lead metal element low specific heat capacity 129 J/(kg·K)

Tap any benchmark above to automatically calculate its exact equivalent in Joule/kilogram kelvin.

ISQ Dimension: [L² T⁻² Θ⁻¹] Coherent SI Unit: joule per kilogram kelvin (J/(kg·K)) Thermodynamics & Heat Transfer

How to Convert Calorie/gram celsius to Joule/kilogram kelvin

Converting Calorie/gram celsius (cal/(g·°C)) to Joule/kilogram kelvin (J/(kg·K)) is a core calculation in Specific Heat Capacity, which measures the thermal energy required to raise the temperature of a unit mass of substance by one degree. Because Calorie/gram celsius represents a larger magnitude than Joule/kilogram kelvin, converting from cal/(g·°C) to J/(kg·K) expands the numerical figure. Exactly 1 Calorie/gram celsius encompasses 4184.000002 Joule/kilogram kelvin. To convert any quantity, multiply the value in Calorie/gram celsius by 4184.000002.

Direct Factor1 cal/(g·°C) = 4184.000002 J/(kg·K)

Inverse Ratio1 J/(kg·K) = 0.000239006 cal/(g·°C)

Conversion ScaleDirect Proportional Magnitude Expansion

First-Principles SI Derivation ProofNIST SP 811 / ISO 80000 Compliance

Mathematical Conversion Derivation via Coherent SI Base Unit

Under the International System of Quantities (ISQ), dimensional conversion between non-SI units is rigorously resolved by bridging through the coherent SI base unit (joule per kilogram kelvin (J/(kg·K))) without arbitrary rounding:

V_{\text{target}} = V_{\text{source}} \times \left( \frac{k_{\text{source} \to \text{SI}}}{k_{\text{target} \to \text{SI}}} \right)

Universal Dimensional Conversion Law (ISO 80000 / NIST SP 811)

1. Source SI Bridge (k_source):1 cal/(g·°C) = 4184.000002 joule per kilogram kelvin (J/(kg·K))

2. Target SI Bridge (k_target):1 J/(kg·K) = 1 joule per kilogram kelvin (J/(kg·K))

Step-by-step substitution for Calorie/gram celsius → Joule/kilogram kelvin:V(J/(kg·K)) = V(cal/(g·°C)) × ( 4184.000002 / 1 ) = V(cal/(g·°C)) × 4184.000002

Mathematical FormulaValue in Joule/kilogram kelvin = Value in Calorie/gram celsius × 4184.00000241Direct computational formula applied for standard conversion.

Worked Example

Evaluating an input of 12 Calorie/gram celsius (cal/(g·°C)) produces 50208.000029 Joule/kilogram kelvin (J/(kg·K)). In heavy-duty utility and industrial workloads, 100 cal/(g·°C) equals 418400.000241 J/(kg·K).

Inverse check: 1 J/(kg·K) = 0.000239006 cal/(g·°C).

Understanding Calorie/gram celsius and Joule/kilogram kelvin

Domain Metrology & Engineering Applications

Governing Law & Equation

Specific Enthalpy Derivative (c_p = (∂h/∂T)_p)

Measurement Instrumentation

Rigorously quantified in laboratory and field settings using differential scanning calorimeters (DSC), adiabatic drop calorimeters, and dual-furnace calorimeter systems.

Primary Industry Sectors

Applied across battery thermal runaway mitigation (EV cell modeling), chemical synthesis reactor safety, molten salt solar storage, and cryogenic coolant engineering under international metrology standard ISO 80000-5:2019, NIST Chemistry WebBook.

Institutional Metrology & Standard Authority:

Formulas, conversion coefficients, and base definitions on this page strictly adhere to the ISO 80000-5:2019, NIST Chemistry WebBook and the BIPM SI Brochure (9th Edition). Governed by Specific Enthalpy Derivative (c_p = (∂h/∂T)_p) under ISO 80000 dimensional vector [L² T⁻² Θ⁻¹].

Multi-Variable Engineering Bridge Thermodynamics & Heat Storage

Specific Heat Capacity to Thermal Energy Storage Bridge (Joules • Kilojoules • Megajoules • kWh • BTU)

Calculate total sensible thermal storage energy Q = c_p × (m × ΔT) for heating or cooling mass charges, bridging specific heat capacity [L² T⁻² Θ⁻¹] with stored thermal energy [M L² T⁻²].

Input Specific Heat Capacity (c_p): cal/(g·°C)

Select Mass × Temperature Delta Product: 2000 kg·K

Governing Law: Q = c_p × (m × ΔT)

Vector: [J/(kg·K)] × [kg·K] → [J]

Live Calculated Bridge Equivalent:

1 cal/(g·°C) at 50 kg Domestic Water at 40K Swing (2,000 kg·K) = 8368000.0048 J

Equals 8368 kJ • 8.368 MJ • 2.324444 kWh

SI Energy

8368000.0048

Joules

Thermal Scale

8368

Kilojoules

Bulk Energy

8.368

Megajoules

Electric Utility Meter

2.324444

kWh

Kilowatt-Hours

Battery Capacity

2324.4444

Watt-Hours

Imperial Thermal

7931.3337

BTU

British Thermal Units

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (J/(kg·K)):
c_p = 1 cal/(g·°C) × 4184.00000241 = 4184.00000241 J/(kg·K)
2. Apply Engineering Parameter (mΔT):
Selected condition: 50 kg Domestic Water at 40K Swing (2,000 kg·K) at mΔT = 2000 kg·K
3. Execute Governing Physical Law in SI Units:
Q = c_p × (m × ΔT) = (4184.00000241 J/(kg·K)) × (2000 kg·K) = 8368000.00482 J
4. Convert to Standard Engineering Units:
• J: 8368000.00482 × 1 = 8368000.0048 J (Joules) • kJ: 8368000.00482 × 0.001 = 8368 kJ (Kilojoules) • MJ: 8368000.00482 × 1 × 10⁻⁶ = 8.368 MJ (Megajoules) • kWh: 8368000.00482 × 2.7778 × 10⁻⁷ = 2.324444 kWh (Kilowatt-Hours) • Wh: 8368000.00482 × 0.0002778 = 2324.4444 Wh (Watt-Hours) • BTU: 8368000.00482 × 0.0009478 = 7931.3337 BTU (British Thermal Units)

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Engineering Substance / Operating Standard	Parameter Value (kg·K)	Reference State / Condition	Typical Industrial & Engineering Application
50 kg Domestic Water at 40K Swing (2,000 kg·K)	`2000`	m = 50 kg, ΔT = 40 K	50-liter domestic hot water tank charge
1,000 kg Hydronic Buffer at 20K Swing (20,000 kg·K)	`20000`	m = 1,000 kg, ΔT = 20 K	Commercial heat pump thermal buffer storage
200 kg Engine Block at 70K Swing (14,000 kg·K)	`14000`	m = 200 kg, ΔT = 70 K	Cast iron engine warm-up heat soak
10,000 kg Process Fluid at 50K Swing (500,000 kg·K)	`500000`	m = 10,000 kg, ΔT = 50 K	Industrial batch chemical reactor heat load

Frequently Asked Questions

There are exactly 4184.00000241 joules/kilogram kelvin (J/(kg·K)) in 1 calorie/gram celsius (cal/(g·°C)). To calculate larger amounts manually, simply multiply your total number of calories (thermochemical)/gram celsius by the conversion multiplier of 4184.00000241.

The mathematical formula to convert calories (thermochemical)/gram celsius to joules/kilogram kelvin is: [value] * 4184.00000241 = joules/kilogram kelvin. Rather than doing the math manually, you can use our high-precision online calculator to process this exact equation instantly without rounding errors.

To perform the reverse calculation from joules/kilogram kelvin back to calories (thermochemical)/gram celsius, you must divide your starting value by 4184.00000241. Our bidirectional tool automatically computes this inverse equation the moment you type into the joule/kilogram kelvin input field.

1 Calorie/gram celsius is larger than 1 Joule/kilogram kelvin. Specifically, 1 Calorie/gram celsius equals exactly 4184.00000241 joules/kilogram kelvin, making it 4184 times larger (a difference of 3.62 orders of magnitude). Therefore, quantities expressed in joules/kilogram kelvin require a larger numerical value to represent the same physical amount.

Under standard international measurement guidelines, 1 Calorie/gram celsius converts to 4184.00000241 joules/kilogram kelvin. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.