Bath Water
Calculate Bath Water instantly with the exact formula and a worked example.
Bath Water
Bathtubs taper toward the bottom, so length × width × depth overestimates the water. This calculator models the sloped sides and turns the result into shower minutes and kWh of heating energy.
How the calculation works
The water in a typical tub is shaped like a prismatoid: two parallel rectangles (the water surface and the flat bottom) joined by sloping walls. The calculator applies the prismatoid (Simpson’s) rule, V = h/6 × (A_top + 4·A_mid + A_bottom), where the middle cross-section uses the average length and average width. Cubic centimeters are divided by 1,000 to give liters (divide by 3.785 if you want US gallons).
Inputs, all in centimeters: inside length and width at the water line, length and width of the flat bottom, and water depth. Shower flow (L/min) lets the tool express one bath as minutes of showering. Cold-water temperature and bath temperature (°C) feed the energy estimate.
Heating energy is Q = V × c × ΔT, with c = 4.186 kJ/(kg·°C) for water and a density of 1 kg per liter; dividing by 3,600 converts kilojoules to kWh. That is the heat that must end up in the water. Your heater’s efficiency and pipe losses come on top.
Worked example
With the defaults — water line 160 × 65 cm, bottom 120 × 45 cm, depth 35 cm — the areas are 10,400 cm² (top), 5,400 cm² (bottom) and 140 × 55 = 7,700 cm² (middle). V = 35/6 × (10,400 + 4 × 7,700 + 5,400) = 271,833 cm³ ≈ 271.8 L (about 72 US gallons). At 9 L/min that equals 30.2 minutes of showering, and heating it from 10 °C to 40 °C takes 271.8 × 4.186 × 30 / 3600 ≈ 9.48 kWh.
Things to keep in mind
- Measure inside the tub at the height you actually fill to, not at the rim. The top few inches of most tubs stay empty.
- Your body displaces roughly one liter per kilogram of body weight, so a filled bath with you in it holds less water than the empty-tub figure.
- A US showerhead is limited to 2.5 gal/min (about 9.5 L/min); WaterSense models use 2.0 gal/min or less. Time a bucket fill to find your real flow.
- To get cost, multiply kWh by your electricity rate and divide by heater efficiency; a gas heater needs more input energy than the number shown here.
- For corner or oval tubs, use the largest rectangle that fits at the water line and at the bottom. The result is then an approximation.
More about: Bath Water
What it calculates
The “Bath Water” calculator computes Water in the bath in L from 8 parameters: length at water level (cm), width at water level (cm), bottom length (cm), bottom width (cm), water depth (cm), shower flow rate (L/min), cold water temperature (°C), bath water temperature (°C).
Estimates environmental impact and carbon footprint.
Example calculation
With parameters Length at water level = 160 cm, Width at water level = 65 cm, Bottom length = 120 cm, Bottom width = 45 cm, Water depth = 35 cm, Shower flow rate = 9 L/min, Cold water temperature = 10 °C, Bath water temperature = 40 °C the result is 271.83 L (Inner dimensions, body volume not included).
How to use
- Enter length at water level, width at water level, bottom length, bottom width, water depth, shower flow rate, cold water temperature and bath water temperature — each field above is adjustable with a slider.
- Water in the bath (L) is calculated automatically as you type.
- Check the worked example below to see the formula applied to real numbers.
- Copy the result or bookmark this calculator.
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FAQ
How much water does a standard bath use?
Is a bath or a shower more water-efficient?
Why is the result lower than the capacity listed by the manufacturer?
Does the energy figure include heat lost while the bath cools?
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