How to Calculate Normal Lapse Rate

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Atmospheric Lapse Rate Calculator

Calculate temperature change based on altitude and normal lapse rate.

Metric (Celsius, Meters) Imperial (Fahrenheit, Feet)
°C
m
m
°C / 1000m
Standard Normal Lapse Rate defaults applied.
Estimated Temperature at Target Altitude
function updateNLRInputs() { var system = document.getElementById("unitSystem").value; var tempLabel = document.getElementById("tempUnitLabel"); var altLabel1 = document.getElementById("altUnitLabel1"); var altLabel2 = document.getElementById("altUnitLabel2"); var rateLabel = document.getElementById("rateUnitLabel"); var rateInput = document.getElementById("lapseRateValue"); var baseTemp = document.getElementById("baseTemperature"); if (system === "metric") { tempLabel.innerText = "°C"; altLabel1.innerText = "m"; altLabel2.innerText = "m"; rateLabel.innerText = "°C / 1000m"; // Set default Normal Lapse Rate for Metric rateInput.value = "6.5"; baseTemp.placeholder = "e.g. 15"; } else { tempLabel.innerText = "°F"; altLabel1.innerText = "ft"; altLabel2.innerText = "ft"; rateLabel.innerText = "°F / 1000ft"; // Set default Normal Lapse Rate for Imperial (approx 3.566°F per 1000ft) rateInput.value = "3.57"; baseTemp.placeholder = "e.g. 59"; } } function calculateLapseRate() { // Inputs var t1 = parseFloat(document.getElementById("baseTemperature").value); var a1 = parseFloat(document.getElementById("baseAltitude").value); var a2 = parseFloat(document.getElementById("targetAltitude").value); var rate = parseFloat(document.getElementById("lapseRateValue").value); var system = document.getElementById("unitSystem").value; // Validation if (isNaN(t1) || isNaN(a1) || isNaN(a2) || isNaN(rate)) { alert("Please enter valid numbers for all fields."); return; } // Logic // The formula for temperature change based on lapse rate is: // T_final = T_initial – (LapseRate * (Altitude_final – Altitude_initial) / 1000) // Note: Lapse rate is positive for cooling with height. var altitudeDiff = a2 – a1; var tempChange = (rate * altitudeDiff) / 1000; var finalTemp = t1 – tempChange; // Formatting var unitSymbol = (system === "metric") ? "°C" : "°F"; var altSymbol = (system === "metric") ? "m" : "ft"; // Display Results var resultDiv = document.getElementById("result"); var finalValueDiv = document.getElementById("finalTempValue"); var detailsDiv = document.getElementById("calculationDetails"); resultDiv.style.display = "block"; finalValueDiv.innerHTML = finalTemp.toFixed(2) + " " + unitSymbol; var direction = (altitudeDiff > 0) ? "ascent" : "descent"; var tempDirection = (tempChange > 0) ? "decrease" : "increase"; // Handle negative temp change display (absolute value for text description) var absTempChange = Math.abs(tempChange); detailsDiv.innerHTML = "Analysis:" + "Altitude Change: " + altitudeDiff + " " + altSymbol + " (" + direction + ")" + "Total Temperature Change: " + (tempChange * -1).toFixed(2) + " " + unitSymbol + "" + "Using a lapse rate of " + rate + " " + unitSymbol + "/1000" + altSymbol + "."; }

How to Calculate Normal Lapse Rate

The Normal Lapse Rate refers to the average rate at which temperature decreases with an increase in altitude within the Earth's troposphere. Understanding this calculation is vital for meteorologists, pilots, mountaineers, and environmental scientists to predict temperature changes at different elevations.

What is the Formula?

To calculate the temperature at a specific altitude using the lapse rate, or to determine the lapse rate between two known points, the following fundamental linear equation is used:

T = T₀ - L × (z - z₀)

  • T = Final Temperature at target altitude
  • T₀ = Initial Temperature at base altitude
  • L = Lapse Rate (degree of temperature change per unit of height)
  • z = Target Altitude
  • z₀ = Base Altitude

Standard Normal Lapse Rate Values

While the actual Environmental Lapse Rate (ELR) fluctuates based on humidity, wind, and local weather conditions, the accepted global averages for the Normal Lapse Rate are:

Measurement System Standard Rate
Metric (SI) 6.5 °C per 1,000 meters (0.65 °C per 100 meters)
Imperial (US) Approx. 3.5 °F per 1,000 feet

Calculation Example

Let's assume you are standing at sea level (0 meters) where the temperature is 20°C. You plan to hike a mountain to an elevation of 2,000 meters. Using the standard normal lapse rate of 6.5°C/1,000m, what will the temperature be at the summit?

  1. Identify Values: T₀ = 20°C, z = 2000m, z₀ = 0m, L = 6.5°C/1000m.
  2. Calculate Altitude Difference: 2000m – 0m = 2000m.
  3. Calculate Temperature Drop: (6.5 ÷ 1000) × 2000 = 13°C drop.
  4. Final Calculation: 20°C – 13°C = 7°C.

The estimated temperature at the summit is 7°C.

Types of Lapse Rates

It is important to distinguish between the "Normal" rate and specific adiabatic rates:

  • Normal Lapse Rate: The long-term average (6.5°C/km).
  • Dry Adiabatic Lapse Rate (DALR): The rate at which dry (unsaturated) air cools as it rises, roughly 9.8°C/km.
  • Moist Adiabatic Lapse Rate (MALR): The rate for saturated air, which varies but averages around 5°C/km due to latent heat release during condensation.

Use the calculator above to adjust the "Lapse Rate" input if you need to calculate specific DALR or MALR scenarios.

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