Dimensional Analysis Calculator
Convert units and analyze physical quantities using dimensional analysis
Unit Conversion
Conversion Result
100 cm
1 m = 100 cm
Quantity: Length [L]
From: meter (m)
To: centimeter (cm)
What is Dimensional Analysis?
Definition
A method to analyze physical quantities in terms of their fundamental dimensions and convert between different unit systems.
Applications
- • Unit conversions
- • Formula verification
- • Error checking
- • Scientific calculations
Base Dimensions
- • [L] - Length
- • [M] - Mass
- • [T] - Time
- • [I] - Current
- • [Θ] - Temperature
Common Conversions
Time Examples:
- • 1 day = 24 hours = 1,440 minutes
- • 1 year ≈ 31,557,600 seconds
- • 1 week = 7 days = 168 hours
Length Examples:
- • 1 km = 1000 m = 0.621 miles
- • 1 inch = 2.54 cm
- • 1 yard = 3 feet = 0.914 m
Force Examples:
- • 1 N = 10⁵ dyne
- • 1 lbf = 4.448 N
- • 1 kgf = 9.807 N
Understanding Dimensional Analysis
The Method
Dimensional analysis uses the principle that physical equations must be dimensionally consistent. This means all terms in an equation must have the same dimensions, and conversion factors can be used to transform quantities from one unit system to another.
Conversion Process
- 1.Identify the dimensional formula of the quantity
- 2.Find the conversion factors between unit systems
- 3.Apply the conversion factors systematically
- 4.Verify dimensional consistency
Dimensional Formulas
Basic Quantities
Area: [L²]
Volume: [L³]
Velocity: [LT⁻¹]
Acceleration: [LT⁻²]
Advanced Quantities
Force: [MLT⁻²]
Energy: [ML²T⁻²]
Power: [ML²T⁻³]
Pressure: [ML⁻¹T⁻²]
Example: Converting Force Units
Problem: Convert 1 Newton to Dynes
Step 1: Identify the dimensional formula for force
Force = [M¹L¹T⁻²]
Step 2: Set up the conversion equation
n₁[M₁¹L₁¹T₁⁻²] = n₂[M₂¹L₂¹T₂⁻²]
Step 3: Substitute known values
• SI system: n₁ = 1 N, M₁ = 1 kg, L₁ = 1 m, T₁ = 1 s
• CGS system: n₂ = ? dyn, M₂ = 1 g, L₂ = 1 cm, T₂ = 1 s
• CGS system: n₂ = ? dyn, M₂ = 1 g, L₂ = 1 cm, T₂ = 1 s
Step 4: Calculate the conversion
n₂ = 1 × (1000/1)¹ × (100/1)¹ × (1/1)⁻² = 10⁵
Result: 1 N = 10⁵ dyn
Result: 1 N = 10⁵ dyn