> ## Documentation Index > Fetch the complete documentation index at: https://voltaire.tevm.sh/llms.txt > Use this file to discover all available pages before exploring further. # Denomination Scale Visualization > Visual guide to Wei, Gwei, and Ether relationships and conversions Run Denomination examples in the interactive playground # 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: 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 ``` ```typescript theme={null} // 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 | *Assuming ETH = \$2,000* ## Conversion Flow Diagrams ### Direct Conversions (Reversible) ``` ┌─────────┐ ×10^9 ┌──────────┐ ×10^9 ┌────────┐ │ 1 Wei │ ─────────────────────> │ 1 Gwei │ ─────────────────────> │ 1 Ether│ └─────────┘ └──────────┘ └────────┘ ^ ^ ^ │ │ │ │ ÷10^9 │ ÷10^9 │ └───────────────────────────────────┴──────────────────────────────────┘ ``` All direct conversions are **reversible without data loss**: * 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) │ └──────────────────┘ ``` **Safe pattern: Always work in smallest unit (Wei) when possible** ## 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 ```typescript theme={null} // 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 ``` ```typescript theme={null} 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? ```typescript theme={null} 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: ```typescript theme={null} 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](/primitives/denomination) - Type definitions * [Conversions](/primitives/denomination/conversions) - Conversion functions * [Gas Calculator](/primitives/denomination/gas-calculator) - Real-world costs * [Usage Patterns](/primitives/denomination/usage-patterns) - Common patterns