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Physics

Sensible Heat Calculator

Calculate the sensible heat gained or lost by any substance using the classic Q = m c ΔT formula, or switch to HVAC airflow mode to size cooling and heating loads using volumetric flow rate. Choose from 15 built-in material presets or enter a custom specific heat, pick metric or imperial units, and select whether to solve for heat, mass, or temperature difference. Results update instantly with a full step-by-step breakdown.

Your details

Physics mode uses a fixed mass. HVAC mode uses volumetric airflow for continuous cooling or heating loads.
Select the unknown you want to calculate; all other fields become inputs.
Mass of the substance being heated or cooled.
kg
Starting temperature of the substance.
°C
Target temperature of the substance. Can be lower than Ti for cooling.
°C
Sensible heat (Q)Heat added
3,347.2kJ

Total heat added (positive) or removed (negative)

Sensible heat (Q)3,172.53BTU
Thermal power-
Thermal power-
Cooling load-
Mass required (m)-
Temperature change (ΔT)80°C
Specific heat used (c)4.184kJ/(kg·K)
Heat (kJ)3,347.2
Heat (BTU)3,172.53
Power (kW)-
Power (BTU/hr)-
02k4k050100
Temperature change ΔT (°C)

3347.2 kJ of sensible heat added to the system.

  • 3347.2 kJ (3172.5 BTU) must be added to the substance.
  • The specific heat used is 4.1840 kJ/(kg·K). Higher specific heat means more energy is needed for the same temperature change.
  • This formula covers sensible heat only - no phase change occurs. If the substance crosses a melting or boiling point, add latent heat separately.

Next stepFor processes near phase-change temperatures, calculate the latent heat of fusion or vaporisation and add it to this result.

Formula

Q=mcpΔT=mcp(TfTi)Q = m \cdot c_p \cdot \Delta T = m \cdot c_p \cdot (T_f - T_i)

Worked example

Heating 10 kg of water from 20 °C to 100 °C: Q = 10 × 4.184 × (100 - 20) = 10 × 4.184 × 80 = 3347 kJ (3172 BTU). In HVAC mode, an airflow of 1000 m³/h with ΔT = 10 °C: Q = 1000 × 1.204 × 1.006 × 10 = 12,112 kJ/h = 3.364 kW.

What is sensible heat?

Sensible heat is thermal energy that changes the temperature of a substance without changing its phase. When you boil water you must first add sensible heat to raise the liquid from room temperature to 100 °C, then add latent heat to drive the phase change. The word "sensible" refers to the fact that this heat can be felt, or sensed, as a temperature rise. It contrasts with latent heat, which is absorbed or released during melting, freezing, condensation, or evaporation at a constant temperature. The governing formula is Q = m c ΔT, where Q is the heat in joules or BTU, m is the mass, c is the specific heat capacity, and ΔT is the temperature change.

Physics mode: Q = mcΔT in detail

In physics mode the calculator solves the standard sensible-heat equation for any one of three unknowns. When solving for heat Q, enter the mass, material (or custom specific heat), initial temperature, and final temperature. To find the mass that would absorb a given heat, set "Solve for" to mass and supply Q, the temperatures, and the material. To find the temperature change produced by a given heat and mass, set "Solve for" to ΔT. A negative result means heat was removed from the system (cooling). The specific heat presets come from NIST data; you can override them with any value for exotic materials. All unit conversions are handled automatically when you switch between metric and imperial.

HVAC mode: sizing cooling and heating loads

HVAC mode replaces the fixed-mass equation with a flow-rate version: Q = V rho c ΔT, where V is the volumetric airflow in m³/h (or CFM), rho is air density, and c is the specific heat of air. The result is given as power in kW and BTU/hr for continuous-load applications, and in tons of refrigeration (TR) for chiller sizing. The standard air density of 1.204 kg/m³ applies at sea level and 20 °C. For high-altitude sites, reduce the density input: air at 1500 m is about 1.056 kg/m³, and at 3000 m about 0.909 kg/m³. The HVAC sensible-heat equation in imperial units is often written as qs = 1.08 x CFM x ΔT(°F), which is the same formula with the constants already combined (0.075 lb/ft³ × 0.24 BTU/lb·°F × 60 min/hr = 1.08).

Sensible heat ratio and total cooling load

In real HVAC systems the total cooling load has two components: sensible heat from temperature differences, and latent heat from the condensation of moisture in the air. The sensible heat ratio (SHR) is defined as SHR = Q_sensible / (Q_sensible + Q_latent). A typical comfort-cooling system has an SHR between 0.70 and 0.90, meaning 70 to 90 percent of its capacity is used to lower temperature and 10 to 30 percent to dehumidify. Spaces with high occupancy, cooking equipment, or open water surfaces have lower SHR values because they release more moisture. This calculator handles only the sensible component; add a latent-heat calculation for the full cooling load.

Specific heat capacities of common materials

Materialcp (kJ/kg·K)cp (BTU/lb·°F)Typical use
Water (liquid)4.1841.000Thermal storage, cooling systems
Ice (0 °C)2.0900.499Cold storage, cryogenics
Ethylene glycol2.4200.578Antifreeze, heat-transfer fluid
Engine oil2.0900.499Lubrication cooling loops
Air (dry)1.0060.240HVAC, ventilation design
Wood (pine)1.7000.406Timber construction thermal mass
Aluminum0.8970.214Heat sinks, cookware
Glass0.8400.201Windows, storage containers
Concrete0.8800.210Building thermal mass
Iron0.4440.106Castings, engine blocks
Steel (mild)0.4900.117Structural, piping
Copper0.3850.092Heat exchangers, wiring
Silver0.2350.056Electronics, high-conductivity parts
Gold0.1290.031High-frequency electronics
Rubber1.7000.406Gaskets, insulation

Values at standard conditions (~20-25 °C). Source: NIST Webbook and Incropera (2007).

Frequently asked questions

What is the difference between sensible heat and latent heat?

Sensible heat changes the temperature of a substance without any phase change, and you can detect the change with a thermometer. Latent heat is absorbed or released during a phase change (melting, boiling, condensing, freezing) at a constant temperature. To heat water from 20 °C to 100 °C you add sensible heat; to then convert it to steam you add latent heat (about 2257 kJ/kg). If the process crosses a phase-change temperature, you must calculate both components and add them together.

What units does this calculator use, and how do I switch?

Use the "Units" selector at the top to toggle between metric (kg, °C, kJ) and imperial (lb, °F, BTU). All input fields and output labels update automatically. Internally, the calculator converts everything to SI, applies Q = m c ΔT, and then converts the result back to the chosen unit system, so switching units never changes the physics.

How do I calculate sensible heat for airflow in an HVAC system?

Switch to "HVAC: airflow-based" mode, enter the volumetric airflow rate (m³/h or CFM), the temperature difference across the coil or space, and optionally adjust air density for altitude. The calculator returns the continuous thermal load in kW, BTU/hr, and tons of refrigeration. In imperial units the shortcut formula qs = 1.08 x CFM x ΔT(°F) is widely used by engineers, and this calculator applies the same relationship through its full derivation.

Why is water's specific heat so high compared to metals?

Water has a specific heat of 4.184 kJ/(kg·K), which is roughly ten times higher than most metals. This is because water molecules form extensive hydrogen-bond networks that must absorb energy before the kinetic motion (temperature) increases. This high specific heat is why water is the default coolant in engines and industrial heat exchangers: a small volume of water can absorb far more heat than the same volume of oil or glycol, though glycol-water mixtures are preferred when frost protection is needed.

What happens if my final temperature is lower than the initial temperature?

A negative ΔT produces a negative Q, which simply means heat is being removed from the substance (cooling). For example, chilling 5 kg of steel from 200 °C to 25 °C gives ΔT = -175 °C and Q = 5 × 0.490 × (-175) = -428.75 kJ: you must extract 428.75 kJ from the steel to cool it. The calculator handles negative values correctly throughout.

How does altitude affect HVAC sensible heat calculations?

Air density drops with altitude. At 1500 m above sea level air density is roughly 1.056 kg/m³ instead of 1.204 kg/m³ at sea level, a reduction of about 12 percent. Because Q = V rho c ΔT, a lower density means a lower heat-transfer capacity for the same airflow. Fans deliver the same volume but move less mass, so HVAC equipment must be derated or oversized. Enter the local air density in the dedicated field to account for this.

Can I solve for mass or temperature change instead of heat?

Yes. In physics mode, use the "Solve for" selector to switch the unknown. Choosing "Mass" lets you enter the heat, material, and temperature range to find how much of that substance you need. Choosing "Temperature change" lets you enter the heat and mass to find the resulting ΔT. The step-by-step panel always mirrors the rearranged formula so you can follow the algebra.

Sources

Written by Dr. Tomás Okafor, PhD Physicist · Lagos, Nigeria

Physicist specializing in classical mechanics, bringing 17 years of research and applied dynamics expertise to every calculator he reviews.

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