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Calories (th)/gram/°C to Kilojoules/kilogram kelvin Converter (cal (th)/(g·°C) to kJ/(kg·K))

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Live Conversion • ISO 80000-5:2019 Certified
1 Calorie (th)/gram/°C = 4.18399538 Kilojoule/kilogram kelvin
1 cal (th)/(g·°C) = 4.183995 kJ/(kg·K) • 1 kJ/(kg·K) = 0.239006 cal (th)/(g·°C)
Calorie (th)/gram/°C to Kilojoule/kilogram kelvin: One Calorie (th)/gram/°C is equal to 4.18399538 Kilojoules/kilogram kelvin.
Certified Authority Value
4.18399538
kJ/(kg·K)
Exact: 1 kJ/(kg·K) ≡ 0.239006 cal (th)/(g·°C)
cal (th)/(g·°C)
cal (th)/(g·°C)
Swap to Kilojoule/kilogram kelvin to Calorie (th)/gram/°C
Swap to Kilojoule/kilogram kelvin to Calorie (th)/gram/°C
kJ/(kg·K)
kJ/(kg·K) 4.18399538
Quick Values:
Conversion Formula
To convert Calorie (th)/gram/°C to Kilojoule/kilogram kelvin, multiply by 4.18399538
cal (th)/(g·°C) × 4.18399538 = kJ/(kg·K)

Calculation: 1 cal (th)/(g·°C) × 4.18399538 = 4.18399538 kJ/(kg·K)

Common Calorie (th)/gram/°C to Kilojoule/kilogram kelvin Calculations

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

Tap any row to calculate
Calorie (th)/gram/°C to Kilojoule/kilogram kelvin: Primary Direct Table (15 Steps)
Calorie (th)/gram/°C to Kilojoule/kilogram kelvin Conversion Reference Table
Conversion & Equivalent Value Scientific Notation
0.001 cal (th)/(g·°C) 0.004184 kJ/(kg·K) 4.184 × 10⁻³
0.01 cal (th)/(g·°C) 0.04184 kJ/(kg·K) 4.184 × 10⁻²
0.1 cal (th)/(g·°C) 0.4184 kJ/(kg·K) 4.184 × 10⁻¹
0.5 cal (th)/(g·°C) 2.091998 kJ/(kg·K) 2.092 × 10⁰
1 cal (th)/(g·°C) 4.183995 kJ/(kg·K) 4.184 × 10⁰
2 cal (th)/(g·°C) 8.367991 kJ/(kg·K) 8.368 × 10⁰
5 cal (th)/(g·°C) 20.919977 kJ/(kg·K) 2.092 × 10¹
10 cal (th)/(g·°C) 41.839954 kJ/(kg·K) 4.184 × 10¹
20 cal (th)/(g·°C) 83.679908 kJ/(kg·K) 8.368 × 10¹
25 cal (th)/(g·°C) 104.599885 kJ/(kg·K) 1.046 × 10²
50 cal (th)/(g·°C) 209.199769 kJ/(kg·K) 2.092 × 10²
100 cal (th)/(g·°C) 418.399538 kJ/(kg·K) 4.184 × 10²
250 cal (th)/(g·°C) 1045.998845 kJ/(kg·K) 1.046 × 10³
500 cal (th)/(g·°C) 2091.99769 kJ/(kg·K) 2.092 × 10³
1000 cal (th)/(g·°C) 4183.995381 kJ/(kg·K) 4.184 × 10³
Kilojoule/kilogram kelvin to Calorie (th)/gram/°C: Reciprocal Summary
Kilojoule/kilogram kelvin to Calorie (th)/gram/°C Conversion Reference Table
Reciprocal & Equivalent Value Scientific Notation
1 kJ/(kg·K) 0.239006 cal (th)/(g·°C) 2.39 × 10⁻¹
5 kJ/(kg·K) 1.19503 cal (th)/(g·°C) 1.195 × 10⁰
10 kJ/(kg·K) 2.39006 cal (th)/(g·°C) 2.39 × 10⁰
50 kJ/(kg·K) 11.9503 cal (th)/(g·°C) 1.195 × 10¹
100 kJ/(kg·K) 23.9006 cal (th)/(g·°C) 2.39 × 10¹
View Complete 15-Row Kilojoule/kilogram kelvin to Calorie (th)/gram/°C 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 (th)/gram/°C (cal (th)/(g·°C)) and Kilojoule/kilogram kelvin (kJ/(kg·K)):

Calorie (th)/gram/°C References:

  • Thermochemical defined calorie baseline for liquid water 1 cal (th)/(g·°C)

Kilojoule/kilogram kelvin References:

  • Liquid water specific heat capacity in thermal engineering 4.184 kJ/(kg·K)
  • Dry steam water vapor at 100 degrees Celsius and 1 atm 2.08 kJ/(kg·K)

Tap any benchmark above to automatically calculate its exact equivalent in Kilojoule/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 (th)/gram/°C to Kilojoule/kilogram kelvin

Converting Calorie (th)/gram/°C (cal (th)/(g·°C)) to Kilojoule/kilogram kelvin (kJ/(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 (th)/gram/°C represents a larger magnitude than Kilojoule/kilogram kelvin, converting from cal (th)/(g·°C) to kJ/(kg·K) expands the numerical figure. Exactly 1 Calorie (th)/gram/°C encompasses 4.183995 Kilojoule/kilogram kelvin. To convert any quantity, multiply the value in Calorie (th)/gram/°C by 4.183995.

Direct Factor1 cal (th)/(g·°C) = 4.183995 kJ/(kg·K)
Inverse Ratio1 kJ/(kg·K) = 0.239006 cal (th)/(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:

Vtarget=Vsource×(ksource→SIktarget→SI)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 (ksource):1 cal (th)/(g·°C) = 4183.995381 joule per kilogram kelvin (J/(kg·K))
2. Target SI Bridge (ktarget):1 kJ/(kg·K) = 1000 joule per kilogram kelvin (J/(kg·K))
Step-by-step substitution for Calorie (th)/gram/°C → Kilojoule/kilogram kelvin:V(kJ/(kg·K)) = V(cal (th)/(g·°C)) × ( 4183.995381 / 1000 ) = V(cal (th)/(g·°C)) × 4.183995
Mathematical FormulaValue in Kilojoule/kilogram kelvin = Value in Calorie (th)/gram/°C × 4.18399538Direct computational formula applied for standard conversion.
Worked Example

For an engineering input of 8 cal (th)/(g·°C), applying the conversion factor yields exactly 33.471963 kJ/(kg·K). At larger operational scale, 10000 Calorie (th)/gram/°C corresponds to 41839.953809 kJ/(kg·K).

Inverse check: 1 kJ/(kg·K) = 0.239006 cal (th)/(g·°C).

Understanding Calorie (th)/gram/°C and Kilojoule/kilogram kelvin

Calorie (th)/gram/°C

cal (th)/(g·°C)
Standard Unit

A Calorie (th)/gram/°C (cal (th)/(g·°C)) is a recognized unit for specific heat capacity.

Applications & Practical Context

In practical specific heat capacity terms, a thermochemical defined calorie baseline for liquid water equals 1 cal (th)/(g·°C).

Physical Setup

A physical magnitude of 1 cal (th)/(g·°C) corresponds to 4183.995381 J/(kg·K) in standard SI measurement.

Conversion to SI Unit: joule per kilogram kelvin (J/(kg·K))
1 cal (th)/(g·°C) = 4183.995381 J/(kg·K)

Kilojoule/kilogram kelvin

kJ/(kg·K)
SI Multiple

A Kilojoule/kilogram kelvin (kJ/(kg·K)) is a decimal multiple of the SI-derived unit for specific heat capacity.

Applications & Practical Context

In practical specific heat capacity terms, a liquid water specific heat capacity in thermal engineering equals 4.184 kJ/(kg·K), a dry steam water vapor at 100 degrees Celsius and 1 atm equals 2.08 kJ/(kg·K).

Physical Setup

A physical magnitude of 1 kJ/(kg·K) corresponds to 1000 J/(kg·K) in standard SI measurement.

Conversion to SI Unit: joule per kilogram kelvin (J/(kg·K))
1 kJ/(kg·K) = 1000 J/(kg·K)

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].

Q = c_p × (m × ΔT)
Vector: [J/(kg·K)] × [kg·K] → [J]
Live Calculated Bridge Equivalent:
1 cal (th)/(g·°C) at 50 kg Domestic Water at 40K Swing (2,000 kg·K) = 8367990.7617 J
Equals 8367.9908 kJ • 8.367991 MJ • 2.324442 kWh
SI Energy
8367990.7617
J
Joules
Thermal Scale
8367.9908
kJ
Kilojoules
Bulk Energy
8.367991
MJ
Megajoules
Electric Utility Meter
2.324442
kWh
Kilowatt-Hours
Battery Capacity
2324.4419
Wh
Watt-Hours
Imperial Thermal
7931.3249
BTU
British Thermal Units
  1. 1. Normalize Input to SI Base Unit (J/(kg·K)):
    c_p = 1 cal (th)/(g·°C) × 4183.99538087 = 4183.99538087 J/(kg·K)
  2. 2. Apply Engineering Parameter (mΔT):
    Selected condition: 50 kg Domestic Water at 40K Swing (2,000 kg·K) at mΔT = 2000 kg·K
  3. 3. Execute Governing Physical Law in SI Units:
    Q = c_p × (m × ΔT) = (4183.99538087 J/(kg·K)) × (2000 kg·K) = 8367990.761738 J
  4. 4. Convert to Standard Engineering Units:
    • J: 8367990.761738 × 1 = 8367990.7617 J (Joules) • kJ: 8367990.761738 × 0.001 = 8367.9908 kJ (Kilojoules) • MJ: 8367990.761738 × 1 × 10⁻⁶ = 8.367991 MJ (Megajoules) • kWh: 8367990.761738 × 2.7778 × 10⁻⁷ = 2.324442 kWh (Kilowatt-Hours) • Wh: 8367990.761738 × 0.0002778 = 2324.4419 Wh (Watt-Hours) • BTU: 8367990.761738 × 0.0009478 = 7931.3249 BTU (British Thermal Units)
Explore Full Energy Converter →
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
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Frequently Asked Questions

There are exactly 4.18399538 kilojoules/kilogram kelvin (kJ/(kg·K)) in 1 calorie (th)/gram/°c (cal (th)/(g·°C)). To calculate larger amounts manually, simply multiply your total number of calories (th)/gram/°c by the conversion multiplier of 4.18399538.

The mathematical formula to convert calories (th)/gram/°c to kilojoules/kilogram kelvin is: [value] * 4.18399538 = kilojoules/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 kilojoules/kilogram kelvin back to calories (th)/gram/°c, you must divide your starting value by 4.18399538. Our bidirectional tool automatically computes this inverse equation the moment you type into the kilojoule/kilogram kelvin input field.

1 Calorie (th)/gram/°C is larger than 1 Kilojoule/kilogram kelvin. Specifically, 1 Calorie (th)/gram/°C equals exactly 4.18399538 kilojoules/kilogram kelvin, making it 4.184 times larger (a difference of 0.62 orders of magnitude). Therefore, quantities expressed in kilojoules/kilogram kelvin require a larger numerical value to represent the same physical amount.

Under standard international measurement guidelines, 1 Calorie (th)/gram/°C converts to 4.18399538 kilojoules/kilogram kelvin. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.