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Denomination Scale Visualization
Understanding the relationships between Wei, Gwei, and Ether with visual guides and scale comparisons.The Denomination Scale
1 Ether (ETH)
|
| = 10^9 Gwei
|
v
1,000,000,000 Gwei
|
| = 10^9 Wei per Gwei
|
v
1,000,000,000,000,000,000 Wei
Linear Scale (Powers of 10)
- Wei to Ether
- Code Scale
Wei: Gwei: Ether:
1 0.000000001 0.000000000000000001
10 0.00000001 0.00000000000000001
100 0.0000001 0.0000000000000001
1,000 0.001 0.000000000001
10,000 0.00001 0.00000000001
100,000 0.0001 0.0000000001
1,000,000 0.01 0.000000001
10,000,000 0.1 0.00000001
100,000,000 1 0.000000001
1,000,000,000 10 0.0000001
10,000,000,000 100 0.000001
100,000,000,000 1,000 0.00001
1,000,000,000,000 10,000 0.0001
10,000,000,000,000 100,000 0.001
100,000,000,000,000 1,000,000 0.01
1,000,000,000,000,000 10,000,000 0.1
10,000,000,000,000,000 100,000,000 1
100,000,000,000,000,000 1,000,000,000 10
1,000,000,000,000,000,000 10,000,000,000 100
// Wei to Ether scale (log10)
const scales = [
{ wei: 1n, gwei: 0.000000001, ether: 0.000000000000000001, name: 'Single Wei' },
{ wei: 1_000_000_000n, gwei: 1, ether: 0.000000001, name: '1 Gwei' },
{ wei: 1_000_000_000_000_000_000n, gwei: 1_000_000_000, ether: 1, name: '1 Ether' },
{ wei: 21_000_000_000_000_000n, gwei: 21_000_000, ether: 0.021, name: 'Transfer' },
{ wei: 1_000_000_000_000_000_000_000n, gwei: 1_000_000_000_000, ether: 1_000, name: '1000 Ether' }
]
scales.forEach(scale => {
console.log(`${scale.name}: ${scale.wei} Wei = ${scale.gwei} Gwei = ${scale.ether} ETH`)
})
Real-World Comparison
Daily Transactions
| Type | Wei | Gwei | Ether | Real Value |
|---|---|---|---|---|
| Dust (spam blocker) | 1,000 | 0.000001 | 0.000000001 | ~$0.000002 |
| Minimum gas (1 gwei) | 1,000,000,000 | 1 | 0.000000001 | ~$0.000002 |
| Min transaction (21k gas @ 1 gwei) | 21,000,000,000 | 0.021 | 0.000000021 | ~$0.00004 |
| Cheap transfer (20 gwei) | 420,000,000,000,000 | 420,000 | 0.00042 | ~$0.84 |
| Normal transfer (50 gwei) | 1,050,000,000,000,000 | 1,050,000 | 0.00105 | ~$2.10 |
| Fast transfer (200 gwei) | 4,200,000,000,000,000 | 4,200,000 | 0.0042 | ~$8.40 |
| Expensive swap (100k gas @ 200 gwei) | 20,000,000,000,000,000 | 20,000,000 | 0.02 | ~$40 |
Conversion Flow Diagrams
Direct Conversions (Reversible)
┌─────────┐ ×10^9 ┌──────────┐ ×10^9 ┌────────┐
│ 1 Wei │ ─────────────────────> │ 1 Gwei │ ─────────────────────> │ 1 Ether│
└─────────┘ └──────────┘ └────────┘
^ ^ ^
│ │ │
│ ÷10^9 │ ÷10^9 │
└───────────────────────────────────┴──────────────────────────────────┘
- 1 Wei → toGwei → Wei = 1 Wei ✓
- 1 Gwei → toWei → Gwei = 1 Gwei ✓
- 1 Ether → toWei → Ether = 1 Ether ✓
Fractional Conversions (Data Loss)
┌──────────────────┐
│ 1.5 Gwei in Wei │ (1,500,000,000 Wei)
│ = 1.5 × 10^9 Wei │
└──────────────────┘
│
│ toGwei (÷10^9)
v
┌──────────────────┐
│ = 1 Gwei │ (truncates .5)
│ (data loss!) │
└──────────────────┘
│
│ toWei (×10^9)
v
┌──────────────────┐
│ = 1,000,000,000 │ (lost 500,000,000 Wei)
│ (NOT 1.5 Gwei) │
└──────────────────┘
Magnitude Comparison
How Small is Wei?
1 Ether = 1,000,000,000,000,000,000 Wei
Like currency: 1 Dollar = 100 Cents = 10,000 Mills
Wei is 18 decimal places smaller than Ether:
Ether.0000000000000000 = Wei
Range: 0 to 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,935
(2^256 - 1 Wei = ~1.16e77)
Scientific Notation
// Understanding big numbers
// 1 Ether
const oneEther = 1_000_000_000_000_000_000n // 1e18 in decimal
// = 10^18 Wei
// 1000 Ether
const thousandEther = 1_000_000_000_000_000_000_000n // 1e21
// = 10^21 Wei
// 1 Million Ether
const millionEther = 1_000_000_000_000_000_000_000_000n // 1e24
// = 10^24 Wei
// Useful conversions
const wei = 1_500_000_000_000_000_000n // 1.5 Ether in Wei
const exponent = 18 // Decimal places for Ether
const ether = Number(wei) / Math.pow(10, exponent) // 1.5
console.log(ether) // 1.5
Gas Price Scale
Understanding how gas prices affect transaction costs:Gas Price Levels (typical mainnet):
Urgent: 200 Gwei ──────────────────┐
│
Fast: 100 Gwei ─────────────┐ │
│ │
Standard: 50 Gwei ──────────┐ │ │
│ │ │
Safe: 20 Gwei ────────┐ │ │ │
│ │ │ │
Slow: 10 Gwei ──────┐ │ │ │ │
│ │ │ │ │
v v v v v
Transfer (21k gas):
Slow: 210,000 Gwei = 0.00021 ETH
Safe: 420,000 Gwei = 0.00042 ETH
Standard: 1,050,000 Gwei = 0.00105 ETH
Fast: 2,100,000 Gwei = 0.0021 ETH
Urgent: 4,200,000 Gwei = 0.0042 ETH
- Cost Impact
- Visual Graph
import * as Gwei from 'tevm/Gwei'
import * as Wei from 'tevm/Wei'
import * as Uint from 'tevm/Uint'
function showCostScale(gasUsed: bigint) {
const prices = [10, 20, 50, 100, 200]
console.log(`Gas amounts: ${gasUsed}`)
console.log('─'.repeat(50))
prices.forEach(gwei => {
const gasPriceWei = Gwei.toWei(Gwei(BigInt(gwei)))
const costWei = Uint.times(gasPriceWei, Uint(gasUsed))
const costGwei = Uint.dividedBy(costWei, Uint(1_000_000_000n))
const costEther = Number(costWei) / 1e18
console.log(`${gwei.toString().padStart(3)} Gwei: ${costGwei} Gwei = ${costEther.toFixed(6)} ETH`)
})
}
// Show scale for transfer (21,000 gas)
showCostScale(21_000n)
console.log()
// Show scale for complex interaction (200,000 gas)
showCostScale(200_000n)
Transfer (21,000 gas) - Cost in Ether:
0.0042 ETH │ ■
│ ■
0.0035 ETH │ ■
│ ■
0.0028 ETH │ ■
│ ■
0.0021 ETH │ ■
│ ■
0.0014 ETH │ ■ ■
│ ■ ■
0.0007 ETH │ ■ ■
│ ■ ■
0 ETH │ ■ ■ ■
└─────────────────
10 20 50 100 200 Gwei
Gas Price
Practical Size Comparisons
What fits in different units?
import * as Wei from 'tevm/Wei'
import * as Gwei from 'tevm/Gwei'
import * as Ether from 'tevm/Ether'
import * as Uint from 'tevm/Uint'
// How much in Wei?
const weiCapacity = Uint(2n ** 256n - 1n) // Max Uint256
// = 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,935 Wei
// = 115,792,089,237 Billion Billion Ether
// Enough for everyone on Earth to have 14+ Ether
// Practical limits
const dappBudget = Ether(1_000_000n) // 1M Ether (huge budget)
const dappBudgetWei = Ether.toWei(dappBudget) // 1e24 Wei
const liquidEthereum = 120_000_000n // All ETH ever (approx)
const liquidWei = Ether.toWei(Ether(liquidEthereum)) // All Wei in existence
Conversion Reference Table
From To Formula Example
─────────────────────────────────────────────────────────────
Wei → Gwei ÷ 10^9 1e9 Wei → 1 Gwei
Wei → Ether ÷ 10^18 1e18 Wei → 1 Ether
Gwei → Wei × 10^9 1 Gwei → 1e9 Wei
Gwei → Ether ÷ 10^9 1e9 Gwei → 1 Ether
Ether → Wei × 10^18 1 Ether → 1e18 Wei
Ether → Gwei × 10^9 1 Ether → 1e9 Gwei
Calculator: Power of 10 Growth
How values grow with each power of 10:const base = 1_000_000_000_000_000_000n // 1 Ether in Wei
// Each step multiplies by 10^9
const wei = base // 10^18 (1 Ether)
const megaWei = base * 1_000n // 10^21
const gigaWei = base * 1_000_000n // 10^24
const teraWei = base * 1_000_000_000n // 10^27
console.log('Growth scale (base = 1 Ether):')
console.log('1x:', wei) // 1 Ether
console.log('1K×:', megaWei) // 1,000 Ether
console.log('1M×:', gigaWei) // 1,000,000 Ether
console.log('1B×:', teraWei) // 1,000,000,000 Ether
Related
- Denomination - Type definitions
- Conversions - Conversion functions
- Gas Calculator - Real-world costs
- Usage Patterns - Common patterns