# Water Heating Energy Calculator

> Computes the energy needed to heat a volume of water by a given temperature rise (specific heat of water 4.186 kJ/(kg·K)) at a heater efficiency, the daily and annual energy and cost for repeated heating, and the heating time for a given heater power.

- Calculator id: `water-heater-energy` · Category: Home Energy & Electrical (`energy`) · Tool name: `calculate_water_heating_energy`
- Canonical page: https://tttkmbb.com/energy/water-heater-energy · This document: https://tttkmbb.com/energy/water-heater-energy.md · JSON definition: https://tttkmbb.com/energy/water-heater-energy.json

## Purpose

Computes the energy needed to heat a volume of water by a given temperature rise (specific heat of water 4.186 kJ/(kg·K)) at a heater efficiency, the daily and annual energy and cost for repeated heating, and the heating time for a given heater power.

**Use when:** You want the energy and cost of hot water for showers, a tank or a kettle, the annual cost of a water heater, or how long a heating element takes to heat a tank.

**Do not use when:** You need standby losses of a storage tank or heat-pump water heater performance under varying conditions (enter its COP × 100 as the efficiency for a rough estimate), or non-water fluids (use specific-heat).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `volume_liters` | number | L | required | Volume of water heated per heating in litres (1 L ≈ 1 kg). (> 0, max 1000000) |
| `temperature_rise_c` | number | °C | required | Temperature increase in °C (or K), e.g. 40 to heat 15 °C mains water to 55 °C. (> 0, max 100) |
| `efficiency_percent` | number | % | optional, default 90 | Share of the purchased energy that ends up in the water: 90–100 electric resistance, 60–95 gas, 200–400 for a heat-pump water heater (COP × 100). (min 10, max 500) |
| `energy_price_per_kwh` | number | per kWh | optional | Optional price per kWh of electricity or gas in your currency, for the daily and annual cost. (min 0, max 100) |
| `heatings_per_day` | number |  | optional, default 1 | How many times per day this volume is heated (e.g. number of showers). (min 0, max 100) |
| `heater_power_kw` | number | kW | optional | Optional heater input power in kW, to report the heating time of one volume. (> 0, max 1000) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `energy_kwh` | number | kWh | 4.186 × volume_liters × temperature_rise_c / 3600 / (efficiency_percent / 100). |
| `energy_mj` | number | MJ | energy_kwh × 3.6. |
| `heat_delivered_kwh` | number | kWh | Useful heat before efficiency losses: 4.186 × volume × ΔT / 3600. |
| `daily_energy_kwh` | number | kWh | energy_kwh × heatings_per_day. |
| `annual_energy_kwh` | number | kWh | daily_energy_kwh × 365. |
| `daily_cost` | number |  | daily_energy_kwh × energy_price_per_kwh; only when a price is given. |
| `annual_cost` | number |  | annual_energy_kwh × energy_price_per_kwh; only when a price is given. |
| `heating_time_hours` | number | h | energy_kwh / heater_power_kw; only when heater_power_kw is given. |

## Formula

`heat_delivered_kwh = 4.186 × volume_liters × temperature_rise_c / 3600; energy_kwh = heat_delivered_kwh / (efficiency_percent / 100); energy_mj = energy_kwh × 3.6; daily_energy_kwh = energy_kwh × heatings_per_day; annual_energy_kwh = daily_energy_kwh × 365; cost = energy × energy_price_per_kwh; heating_time_hours = energy_kwh / heater_power_kw`

Q = m·c·ΔT with c = 4.186 kJ/(kg·K) and 1 kg per litre (density variation with temperature ignored, < 2 %). The efficiency converts delivered heat into purchased energy; storage standby losses are not included.

## Data Sources

- Wikipedia – Specific heat capacity — https://en.wikipedia.org/wiki/Specific_heat_capacity (reference, retrieved 2026-09-24)
- U.S. DOE Energy Saver – Sizing a New Water Heater — https://www.energy.gov/energysaver/sizing-new-water-heater (government, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/water-heater-energy?volume_liters=…&temperature_rise_c=…`
- `POST https://tttkmbb.com/api/v1/calculate/water-heater-energy` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/water-heater-energy · OpenAPI operationId `calculate_water_heating_energy` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "water-heater-energy", "inputs": {…}}`

## Example

- 50 L by 40 °C at 100 % efficiency: inputs `{"volume_liters":50,"temperature_rise_c":40,"efficiency_percent":100}` → `{"energy_kwh":2.326,"energy_mj":8.372,"heat_delivered_kwh":2.326,"annual_energy_kwh":848.8}`
- 50 L by 40 °C at 90 %, twice a day, 0.30 per kWh, 2 kW element: inputs `{"volume_liters":50,"temperature_rise_c":40,"efficiency_percent":90,"energy_price_per_kwh":0.3,"heatings_per_day":2,"heater_power_kw":2}` → `{"energy_kwh":2.584,"daily_energy_kwh":5.168,"annual_energy_kwh":1886.3,"daily_cost":1.55,"annual_cost":565.89,"heating_time_hours":1.29}`

```
GET https://tttkmbb.com/api/v1/calculate/water-heater-energy?volume_liters=50&temperature_rise_c=40&efficiency_percent=100
```

## Limitations

You need standby losses of a storage tank or heat-pump water heater performance under varying conditions (enter its COP × 100 as the efficiency for a rough estimate), or non-water fluids (use specific-heat). Q = m·c·ΔT with c = 4.186 kJ/(kg·K) and 1 kg per litre (density variation with temperature ignored, < 2 %). The efficiency converts delivered heat into purchased energy; storage standby losses are not included. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**How much energy does a shower use?**

A 10-minute shower at 9 L/min uses 90 L; heating it from 15 °C to 40 °C (ΔT 25 K) needs 2.6 kWh of heat, about 2.9 kWh of electricity at 90 % efficiency.

**How do I model a heat-pump water heater?**

Enter its coefficient of performance times 100 as efficiency_percent (COP 3 → 300 %); the calculator then divides the heat by 3.

**Why does a gas heater cost less despite lower efficiency?**

Efficiency converts heat to purchased energy; cost also depends on the price per kWh, and gas is usually cheaper per kWh than electricity. Enter the gas price per kWh (price per m³ ÷ ≈ 10.5 kWh/m³).

## Related

- [Specific Heat Calculator](https://tttkmbb.com/physics/specific-heat.md) — Heat energy for other substances and units.
- [Electricity Cost Calculator](https://tttkmbb.com/everyday/electricity-cost.md) — Cost of the kWh at several tariffs.
- [Solar Payback Calculator](https://tttkmbb.com/energy/solar-payback.md) — Solar electricity that could supply the water heater.