Water Balance Calculator
Runoff Coefficient & Infiltration Rate
Rational Method - Peak Runoff
Green-Ampt Infiltration
| Land Cover / Surface | Runoff Coefficient C | Typical Infiltration (mm/hr) | NRCS Soil Group |
|---|---|---|---|
| Concrete / Asphalt | 0.85 – 0.95 | 0 – 2 | - |
| Rooftops | 0.75 – 0.95 | 0 – 5 | - |
| Lawns / Turf (sandy) | 0.10 – 0.20 | 25 – 50 | A |
| Lawns / Turf (clay) | 0.25 – 0.35 | 2 – 5 | D |
| Row Crops | 0.25 – 0.50 | 5 – 15 | B/C |
| Forest / Woodland | 0.05 – 0.25 | 30 – 120 | A/B |
| Meadow / Prairie | 0.10 – 0.30 | 20 – 50 | A/B |
Monthly Water Budget
Enter monthly precipitation and ET values to get full-year water balance and deficit/surplus analysis. Units: mm.
| Month | P (mm) | ET (mm) | ΔS (mm) | Cum. ΔS (mm) | Status |
|---|---|---|---|---|---|
| Annual Total | - | - | - | - | |
Rainwater Harvesting Calculator
Theory, Formulas & Hydrology Concepts
Water management is the coordinated planning, development, and use of water resources to meet human needs while sustaining ecosystems. The foundation is the hydrological cycle - the continuous movement of water through precipitation, runoff, infiltration, evapotranspiration, and groundwater recharge.
The water budget is governed by conservation of mass applied to a defined control volume (watershed, basin, or aquifer):
ΔS = Change in Storage | P = Precipitation | R = Runoff | ET = Evapotranspiration | G = Groundwater Outflow
For a closed watershed with negligible groundwater exchange, G ≈ 0 and the equation simplifies to ΔS = P − R − ET. Positive ΔS means storage is increasing (aquifer recharge, soil moisture gain); negative ΔS means depletion.
Q = Peak runoff (m³/s) | C = Runoff coefficient (dimensionless) | i = Rainfall intensity (mm/hr) | A = Area (ha)
The rational method (ASCE, 1996) is applicable for urban drainage basins < 80 ha. The runoff coefficient C depends on land use, soil type, and slope.
The FAO-56 Penman-Monteith equation is the global standard for reference evapotranspiration ET₀:
Δ = slope of saturation vapour pressure curve | Rn = net radiation | γ = psychrometric constant | u₂ = wind speed | es,ea = vapour pressures
f = infiltration rate (mm/hr) | Ks = saturated hydraulic conductivity | ψ = suction head | Δθ = moisture deficit | F = cumulative infiltration
V = harvestable volume (m³) | P = annual rainfall (m) | A = catchment area (m²) | C_r = roof runoff coefficient | n = rain events | V_ff = first-flush discard per event
| Process | Description | Typical Magnitude | Key Variables |
|---|---|---|---|
| Precipitation | Water falling as rain, snow, sleet, or hail | 250–3000 mm/yr globally | Intensity, duration, frequency |
| Evaporation | Liquid water → vapour from open water surfaces | 500–2000 mm/yr | Temperature, wind, humidity |
| Transpiration | Water vapour lost through plant stomata | ~70% of global ET | LAI, stomatal resistance |
| Infiltration | Water entering the soil surface | 2–120 mm/hr depending on soil | Soil texture, moisture, compaction |
| Runoff | Surface flow when precipitation exceeds infiltration | 10–50% of P in humid climates | C, slope, land use |
| Groundwater Flow | Subsurface lateral movement of water | 0–1 m/day in aquifers | Hydraulic gradient, permeability |
| Percolation | Downward movement through unsaturated zone | Depends on soil texture | Matric potential, gravity |
A watershed (catchment or drainage basin) is the area that drains to a common outlet. The watershed divide is the topographic boundary separating adjacent basins. Key characteristics: area (km²), shape factor, drainage density (km/km²), channel slope, and land use.
The time of concentration (Tc) is the time for runoff to travel from the hydraulically most distant point to the outlet:
L = channel length (m) | S = channel slope (m/m)
| Category | Annual Per Capita Water (m³) | Condition |
|---|---|---|
| Absolute Scarcity | < 500 | Severe humanitarian risk |
| Scarcity | 500 – 1,000 | Major constraints on development |
| Stress | 1,000 – 1,700 | Regular water stress episodes |
| Sufficient | 1,700 – 4,000 | Generally adequate but localised problems |
| Abundant | > 4,000 | No significant scarcity |
Frequently Asked Questions
1. What is the water balance equation and what does each term mean?
The water balance equation ΔS = P − R − ET (or P = R + ET + ΔS) applies conservation of mass to a watershed. P (precipitation) is total water input; R (runoff) is surface and subsurface flow leaving the basin; ET (evapotranspiration) is water returned to the atmosphere by evaporation from land and water plus transpiration from plants; ΔS (change in storage) represents net change in soil moisture, groundwater, and surface water storage. If ΔS > 0, the basin is gaining water; if ΔS < 0, it is losing stored water.
2. What is the difference between evaporation and evapotranspiration (ET)?
Evaporation is the physical process of liquid water converting to water vapour from bare soil, open water, and wet surfaces. Evapotranspiration (ET) is the combined total of evaporation plus transpiration - the water released by plant leaves through stomata as part of photosynthesis and metabolic processes. In vegetated watersheds, transpiration can account for 70% or more of total ET. Reference ET (ET₀) is calculated for a hypothetical 0.12 m tall grass crop under standard conditions using the FAO-56 Penman-Monteith equation.
3. What is the rational method and when is it used?
The rational method (Q = C×i×A/360) estimates peak stormwater runoff rate from small urban catchments (generally <80 hectares). Q is peak discharge in m³/s, C is the dimensionless runoff coefficient (reflecting land use and soil permeability), i is rainfall intensity in mm/hr for a storm of duration equal to the time of concentration, and A is catchment area in hectares. It is widely used for storm drain design, culvert sizing, and stormwater management in urban planning.
4. How does the Green-Ampt infiltration model work?
The Green-Ampt model is a physically-based infiltration model that treats the soil as having a sharp wetting front moving downward. It computes infiltration rate f = Ks × [1 + (ψ × Δθ)/F(t)], where Ks is saturated hydraulic conductivity, ψ is the capillary suction head at the wetting front, Δθ is the initial moisture deficit (porosity minus initial moisture content), and F(t) is cumulative infiltration depth. As F increases, the infiltration rate decreases toward Ks. It is more accurate than the simpler Philip or Horton models for soils where capillary suction is important.
5. What is the difference between a well and a watershed?
A watershed (also called a catchment, drainage basin, or river basin) is a land area defined by topography where all precipitation drains to a common outlet point (river, lake, or ocean). A well is an engineered structure drilled or dug into an aquifer to extract groundwater. Watersheds are delineated using topographic maps or digital elevation models (DEMs) and are the fundamental spatial unit for water resources management and hydrological analysis.
6. How do I calculate rainwater harvesting potential for my roof?
Use: V = P × A × C_r − (n × V_ff). V is harvestable annual volume in litres, P is annual rainfall in metres, A is roof catchment area in m², C_r is the runoff coefficient for the roof surface (0.7–0.95 for tiles and metal, 0.5–0.7 for rough surfaces), n is the number of rain events per year, and V_ff is the first-flush discard volume per event in litres (typically 0.2–0.4 L per m² of roof per event). The first-flush removes the most polluted initial runoff which carries bird droppings, dust, and roof debris.
7. What causes water scarcity and how is it measured?
Water scarcity occurs when freshwater demand exceeds available supply, or when poor quality makes water unusable. It is measured per capita: absolute scarcity <500 m³/person/year, scarcity 500–1000, stress 1000–1700. Causes: population growth, agriculture (70% of global freshwater use), climate change altering precipitation patterns, pollution reducing usable supplies, poor water governance, and infrastructure gaps. Over 2 billion people live in countries experiencing water stress, according to UNEP.
8. What is evapotranspiration's role in the water balance?
ET is typically the largest water loss component in most terrestrial water budgets, often representing 60–80% of annual precipitation in humid climates and >100% of precipitation in arid regions (drawn from storage). Understanding ET is critical for irrigation scheduling, drought monitoring, and hydrological modelling. Globally, ET returns about 40% of precipitation back to the atmosphere, making it a key driver of regional climate patterns and feedback loops.
9. What two processes in the water cycle move water upward against gravity?
Evaporation (liquid water converting to vapour driven by solar energy and vapour pressure gradients) and transpiration (water drawn upward through plant roots, stems, and leaves and released as vapour through stomata). Both processes move water from Earth's surface upward into the atmosphere, directly counteracting gravity. These are often collectively called evapotranspiration (ET) in hydrological analysis.
10. How does land use change affect the water budget?
Urbanisation (replacing vegetation and permeable soil with impervious surfaces) dramatically increases runoff (C rises from 0.1 to 0.9), reduces infiltration, decreases ET (less vegetation), and reduces groundwater recharge. Deforestation increases runoff and reduces ET. Agricultural irrigation increases ET above natural levels. Reforestation increases ET, infiltration, and groundwater recharge while reducing peak runoff. These land-use feedbacks are central to integrated watershed management planning.
11. What is floodplain management?
Floodplain management is a set of strategies to reduce flood risk, protect ecosystems, and guide land use in areas adjacent to rivers that are subject to periodic inundation. Measures include: zoning regulations (restricting development in high-risk zones), detention basins (ponding areas that attenuate peak flows), channel modifications (levees, bypass channels), natural flood management (restoring floodplain connectivity, wetland restoration), and early warning systems. FEMA's National Flood Insurance Program (NFIP) in the US maps flood zones and requires floodplain management ordinances for participating communities.
12. What is infiltration rate and how is it measured?
Infiltration rate is the speed at which water enters the soil surface, measured in mm/hr or cm/hr. It is highest at the start of a storm (when soil is dry) and decreases toward the saturated hydraulic conductivity Ks as soil wets up. Measured in the field using a double-ring infiltrometer (two concentric steel rings driven into soil, water maintained in both rings, inner ring rate measured) or by a tension infiltrometer. Typical values: sand 25–250 mm/hr, loam 10–25 mm/hr, clay <5 mm/hr.
13. How can I conserve water at home?
Effective household water conservation measures include: installing low-flow fixtures (shower heads <8 L/min, dual-flush toilets <6 L/flush); fixing leaks (a dripping tap wastes 11,000 L/year); rainwater harvesting for garden use; grey water recycling (reuse shower/sink water for toilet flushing); drought-tolerant landscaping (xeriscaping reduces outdoor water use by 50–75%); using dishwashers/washing machines only when full; and timing irrigation in the early morning or evening to reduce evaporation losses.
14. What is integrated water resources management (IWRM)?
IWRM is a process that promotes the coordinated development and management of water, land, and related resources to maximise economic and social welfare without compromising the sustainability of vital ecosystems. It recognises: water is a finite shared resource; water has economic, social, and environmental value; all sectors (agriculture, energy, urban, ecosystems) must be coordinated; governance should involve all stakeholders. IWRM was formalised at the Dublin Principles (1992) and integrated into the UN Sustainable Development Goals (SDG 6: Clean Water and Sanitation).
15. What is groundwater and how does it relate to the water budget?
Groundwater is freshwater stored in aquifers (porous rock or sediment formations) below the water table. It is recharged by infiltration from precipitation, rivers, and lakes (the G recharge term in the full water balance). Groundwater discharge occurs to rivers (baseflow), springs, and through pumped wells. Many rivers maintain flow during dry periods through groundwater baseflow. Overextraction of groundwater beyond recharge rates causes water table decline, land subsidence, and aquifer depletion - a critical global sustainability issue with 30% of global freshwater withdrawals from non-renewable aquifer storage.