CALCULATORS / BUILDINGS, HVAC AND COMFORT

Water heating energy and recovery calculator

Well-mixed water heating; constant heat capacity and efficiency.

hvac-water-heating.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	energykWh	durations
	2.33333	4666.67
	1.86667	3733.33

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

heat-up time budget4666.67 s✓ passes

BASELINE INPUTS

volume50 Ldensity1000 kg/m^3heatCapacity4200 J/(kg*K)rise40 Kpower2000 Wefficiency0.9

CALCULATED

energy2.3333 kWh

duration4666.7 s

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Water heating energy and recovery
# Scope: Well-mixed water heating; constant heat capacity and efficiency.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

volume = 50 L
density = 1000 kg/m^3
heatCapacity = 4200 J/(kg*K)
rise = 40 K
power = 2000 W
efficiency = 0.9

energy := volume*density*heatCapacity*rise [kWh]
duration := energy/(power*efficiency) [s]

check heat-up time budget: duration <= 5400.0 s

scenario alternative: volume = 40 L

Calculated from your source · not saved

Baseline · Baseline

heat-up time budget4666.67 s ✓ passes

alternative · alternative

heat-up time budget3733.33 s ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

energy: energy = volume*density*heatCapacity*rise [kWh]
duration: duration = energy/(power*efficiency) [s]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

volume: 50 L
density: 1000 kg/m^3
heat capacity: 4200 J/(kg*K)
rise: 40 K
power: 2000 W
efficiency: 0.9

Calculated

energy: 2.33333 kWh
duration: 4666.67 s

Assumptions and limits

Well-mixed water heating; constant heat capacity and efficiency.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Water heating energy and recovery. Inputs: water volume; temperatures; heater efficiency and power. Outputs: energy; reheat time. Model scope: Simplified heat and moisture balances; site-specific assumptions. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: water volume, temperatures, heater efficiency and power
Outputs: energy, reheat time
Modes: calculate, compare, sweep
Drawing: Building heat-flow diagram

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS